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andrea semanicova
  • Kosice, Kosice, Slovakia
Let G = (V, E) be a finite simple undirected graph without K2 components. A bijection f : E → {1, 2, ⋯, |E|} is called a local antimagic labeling if for any two adjacent vertices u and v, they have different vertex sums, i.e., w(u) ≠... more
Let G = (V, E) be a finite simple undirected graph without K2 components. A bijection f : E → {1, 2, ⋯, |E|} is called a local antimagic labeling if for any two adjacent vertices u and v, they have different vertex sums, i.e., w(u) ≠ w(v), where the vertex sum w(u) = ∑e∈E(u) f(e), and E(u) is the set of edges incident to u. Thus any local antimagic labeling induces a proper vertex coloring of G where the vertex v is assigned the color (vertex sum) w(v). The local antimagic chromatic number χla(G) is the minimum number of colors taken over all colorings induced by local antimagic labelings of G. It was conjectured [6] that for every tree T the local antimagic chromatic number l + 1 ≤ χla(T) ≤ l + 2, where l is the number of leaves of T. In this article we verify the above conjecture for complete full t-ary trees, for t ≥ 2. A complete full t-ary tree is a rooted tree in which all nodes have exactly t children except leaves and every leaf is of the same depth. In particular we obtain ...
A k-labeling from the vertex set of a simple graph G=(V,E) to a set of integers {1,2,…,k} is defined to be a modular edge irregular if, for every couple of distinct edges, their modular edge weights are distinct. The modular edge weight... more
A k-labeling from the vertex set of a simple graph G=(V,E) to a set of integers {1,2,…,k} is defined to be a modular edge irregular if, for every couple of distinct edges, their modular edge weights are distinct. The modular edge weight is the remainder of the division of the sum of end vertex labels by modulo |E(G)|. The modular edge irregularity strength of a graph is known as the maximal vertex label k, minimized over all modular edge irregular k-labelings of the graph. In this paper we describe labeling schemes with symmetrical distribution of even and odd edge weights and investigate the existence of (modular) edge irregular labelings of joins of paths and cycles with isolated vertices. We estimate the bounds of the (modular) edge irregularity strength for the join graphs Pn+Km¯ and Cn+Km¯ and determine the corresponding exact value of the (modular) edge irregularity strength for some fan graphs and wheel graphs in order to prove the sharpness of the presented bounds.
An edge labeling of a graph G=(V,E) using every label from the set {1,2,⋯,|E(G)|} exactly once is a local antimagic labeling if the vertex-weights are distinct for every pair of neighboring vertices, where a vertex-weight is the sum of... more
An edge labeling of a graph G=(V,E) using every label from the set {1,2,⋯,|E(G)|} exactly once is a local antimagic labeling if the vertex-weights are distinct for every pair of neighboring vertices, where a vertex-weight is the sum of labels of all edges incident with that vertex. Any local antimagic labeling induces a proper vertex coloring of G where the color of a vertex is its vertex-weight. This naturally leads to the concept of a local antimagic chromatic number. The local antimagic chromatic number is defined to be the minimum number of colors taken over all colorings of G induced by local antimagic labelings of G. In this paper, we estimate the bounds of the local antimagic chromatic number for disjoint union of multiple copies of a graph.
A simple graph G = (V,E) admits an H-covering if every edge in E belongs to a subgraph of G isomorphic to a given graph H . Then the graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . .... more
A simple graph G = (V,E) admits an H-covering if every edge in E belongs to a subgraph of G isomorphic to a given graph H . Then the graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs ∗ Corresponding author. P. JAYANTHI ET AL. /AUSTRALAS. J. COMBIN. 67 (1) (2017), 46–64 47 H ′ of G isomorphic to H , the H ′-weights, wtf(H ′) = ∑ v∈V (H′) f(v) + ∑ e∈E(H′) f(e), form an arithmetic progression a, a + d, a + 2d, . . . , a + (t − 1)d where a is the first term, d is the common difference and t is the number of subgraphs of G isomorphic to H . Such a labeling is called super if f(V ) = {1, 2, . . . , |V |}. This paper deals with some results on anti-balanced sets and we show the existence of super (a, d)-cycle-antimagic labelings of fans and some square graphs.
Let G=(V,E) be a simple graph. A vertex labeling f:V(G)→{1,2,⋯,k} is defined to be a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of a graph G if for any two adjacent vertices x,y∈V(G) their weights... more
Let G=(V,E) be a simple graph. A vertex labeling f:V(G)→{1,2,⋯,k} is defined to be a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of a graph G if for any two adjacent vertices x,y∈V(G) their weights are distinct, where the weight of a vertex x∈V(G) is the sum of all labels of vertices whose distance from x is at most d (respectively, at most d but at least 1). The minimum k for which there exists a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of G is called the local inclusive (respectively, non-inclusive) d-distance vertex irregularity strength of G. In this paper, we present several basic results on the local inclusive d-distance vertex irregularity strength for d=1 and determine the precise values of the corresponding graph invariant for certain families of graphs.
A simple graph G = (V,E) admits an H-covering if every edge in E belongs at least to one subgraph of G isomorphic to a given graph H . Then the graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E →... more
A simple graph G = (V,E) admits an H-covering if every edge in E belongs at least to one subgraph of G isomorphic to a given graph H . Then the graph G admitting an H-covering is (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs H ′ of G isomorphic to H , the H ′-weights, wtf(H ′) = ∑ v∈V (H′) f(v) + ∑ e∈E(H′) f(e), form an arithmetic progression with the initial term a and the common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. This paper is devoted to studying the existence of super (a, d)-Hantimagic labelings for fans when subgraphs H are cycles.
Let $D$ be a digraph, possibly with loops. A queen labeling of $D$ is a bijective function $l:V(G)\longrightarrow \{1,2,\ldots,|V(G)|\}$ such that, for every pair of arcs in $E(D)$, namely $(u,v)$ and $(u',v')$ we have (i)... more
Let $D$ be a digraph, possibly with loops. A queen labeling of $D$ is a bijective function $l:V(G)\longrightarrow \{1,2,\ldots,|V(G)|\}$ such that, for every pair of arcs in $E(D)$, namely $(u,v)$ and $(u',v')$ we have (i) $l(u)+l(v)\neq l(u')+l(v')$ and (ii) $l(v)-l(u)\neq l(v')-l(u')$. Similarly, if the two conditions are satisfied modulo $n=|V(G)|$, we define a modular queen labeling. There is a bijection between (modular) queen labelings of $1$-regular digraphs and the solutions of the (modular) $n$-queens problem. The $\otimes_h$-product was introduced in 2008 as a generalization of the Kronecker product and since then, many relations among labelings have been established using the $\otimes_h$-product and some particular families of graphs. In this paper, we study some families of $1$-regular digraphs that admit (modular) queen labelings and present a new construction concerning to the (modular) $n$-queens problem in terms of the $\otimes_h$-product, whi...
In this work, we introduce a new topological index called a general power sum-connectivity index and we discuss this graph invariant for some classes of extremal graphs. This index is defined by Y α G = ∑ u v ∈ E G d u d u + d v d v α ,... more
In this work, we introduce a new topological index called a general power sum-connectivity index and we discuss this graph invariant for some classes of extremal graphs. This index is defined by Y α G = ∑ u v ∈ E G d u d u + d v d v α , where d u and d v represent the degree of vertices u and v , respectively, and α ≥ 1 . A connected graph G is called a k -generalized quasi-tree if there exists a subset V k ⊂ V G of cardinality k such that the graph G − V k is a tree but for any subset V k − 1 ⊂ V G of cardinality k − 1 , the graph G − V k − 1 is not a tree. In this work, we find a sharp lower and some sharp upper bounds for this new sum-connectivity index.
A simple graph $G=(V,E)$ admits an~$H$-covering if every edge in $E$ belongs to at least one subgraph of $G$ isomorphic to a given graph $H$. The graph $G$ admitting an $H$-covering is $(a,d)$-$H$-antimagic if there exists... more
A simple graph $G=(V,E)$ admits an~$H$-covering if every edge in $E$ belongs to at least one subgraph of $G$ isomorphic to a given graph $H$. The graph $G$ admitting an $H$-covering is $(a,d)$-$H$-antimagic if there exists a~bijection $f:V\cup E\to\{1,2,\cdots,|V|+|E|\}$ such that, for all subgraphs $H'$ of $G$ isomorphic to $H$, the $H'$-weights, $wt_f(H')= \sum_{v\in V(H')} f(v) + \sum_{e\in E(H')} f(e)$, form an~arithmetic progression with the initial term $a$ and the common difference $d$. Such a labeling is called {\it super} if the smallest possible labels appear on the vertices. In this paper we prove the existence of super $(a,d)$-$H$-antimagic labelings of fan graphs and ladders for $H$ isomorphic to a cycle.
A simple graphG= (V,E) admits anH-covering, if every edge inE(G) belongs to a subgraph ofGisomorphic toH. A graphGadmitting anH-covering is called an (a,d)-H-antimagic if there exists a bijective functionf:V(G) ∪E(G) → {1, 2, …, |V(G)| +... more
A simple graphG= (V,E) admits anH-covering, if every edge inE(G) belongs to a subgraph ofGisomorphic toH. A graphGadmitting anH-covering is called an (a,d)-H-antimagic if there exists a bijective functionf:V(G) ∪E(G) → {1, 2, …, |V(G)| + |E(G)|} such that for all subgraphsH′ isomorphic toHthe sums ∑v∈V(H′)f(v) + ∑e∈E(H′)f(e) form an arithmetic sequence {a,a+d, …,a+ (t− 1)d}, wherea> 0 andd≥ 0 are integers andtis the number of all subgraphs ofGisomorphic toH. Moreover, if the vertices are labeled with numbers 1, 2, …, |V(G)| the graph is called super. In this paper we deal with super cycle-antimagicness of subdivided graphs. We also prove that the subdivided wheel admits an (a,d)-cycle-antimagic labeling for somed.
A simple graph $G=(V,E)$ admits an $H$-covering if every edge in $E$ belongs to at least one subgraph of $G$ isomorphic to a given graph $H$. Then the graph $G$ is $(a,d)$-$H$-antimagic if there exists a bijection $f:V\cup E\rightarrow... more
A simple graph $G=(V,E)$ admits an $H$-covering if every edge in $E$ belongs to at least one subgraph of $G$ isomorphic to a given graph $H$. Then the graph $G$ is $(a,d)$-$H$-antimagic if there exists a bijection $f:V\cup E\rightarrow \{1,2,\ldots ,|V|+|E|\}$ such that, for all subgraphs $H^{\prime }$ of $G$ isomorphic to $H$, the $H^{\prime }$-weights, $wt_{f}(H^{\prime })=\sum _{v\in V(H^{\prime })}f(v)+\sum _{e\in E(H^{\prime })}f(e)$, form an arithmetic progression with the initial term $a$ and the common difference $d$. When $f(V)=\{1,2,\ldots ,|V|\}$, then $G$ is said to be super $(a,d)$-$H$-antimagic. In this paper, we study super $(a,d)$-$H$-antimagic labellings of a disjoint union of graphs for $d=|E(H)|-|V(H)|$.
An(a,s)-vertex-antimagic edge labeling(or an(a,s)-VAElabeling, for short) ofGis a bijective mapping from the edge setE(G)of a graphGto the set of integers1,2,…,|E(G)|with the property that the vertex-weights form an arithmetic sequence... more
An(a,s)-vertex-antimagic edge labeling(or an(a,s)-VAElabeling, for short) ofGis a bijective mapping from the edge setE(G)of a graphGto the set of integers1,2,…,|E(G)|with the property that the vertex-weights form an arithmetic sequence starting fromaand having common differences, whereaandsare two positive integers, and the vertex-weight is the sum of the labels of all edges incident to the vertex. A graph is called(a,s)-antimagic if it admits an(a,s)-VAElabeling. In this paper, we investigate the existence of(a,1)-VAE labeling for disconnected 3-regular graphs. Also, we define and study a new concept(a,s)-vertex-antimagic edge deficiency, as an extension of(a,s)-VAE labeling, for measuring how close a graph is away from being an(a,s)-antimagic graph. Furthermore, the(a,1)-VAE deficiency of Hamiltonian regular graphs of even degree is completely determined. More open problems are mentioned in the concluding remarks.
Research Interests:
A simple graphGadmits anH-covering if every edge inE(G)belongs to a subgraph ofGisomorphic toH. The graphGis said to be (a,d)-H-antimagic if there exists a bijection from the vertex setV(G)and the edge setE(G)onto the set of... more
A simple graphGadmits anH-covering if every edge inE(G)belongs to a subgraph ofGisomorphic toH. The graphGis said to be (a,d)-H-antimagic if there exists a bijection from the vertex setV(G)and the edge setE(G)onto the set of integers1, 2, …,VG+E(G)such that, for all subgraphsH′ofGisomorphic toH, the sum of labels of all vertices and edges belonging toH′constitute the arithmetic progression with the initial termaand the common differenced.Gis said to be a super (a,d)-H-antimagic if the smallest possible labels appear on the vertices. In this paper, we study super tree-antimagic total labelings of disjoint union of graphs.
The concept of face-antimagic labeling of plane graphs was introduced by Mirka Miller in 2003. This survey aims to give an overview of the recent results obtained in this topic. 1 Corresponding author. Department of Applied Mathematics... more
The concept of face-antimagic labeling of plane graphs was introduced by Mirka Miller in 2003. This survey aims to give an overview of the recent results obtained in this topic. 1 Corresponding author. Department of Applied Mathematics and Informatics, Technical University, Letná 9, Košice, Slovakia. martin.baca@tuke.sk 2 Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia. ebaskoro@math.itb.ac.id or ebaskoro@gmail.com 3 School of Electrical Engineering and Computer Science, The University of Newcastle, NSW 2308, Australia. ljiljana.brankovic@newcastle.edu.au 4 Institute of Mathematics, P.J. Šafárik University, Jesenná 5, Košice, Slovakia. stanislav.jendrol@upjs.sk 5 School of Electrical Engineering and Computer Science, The University of Newcastle, NSW 2308, Australia. yuqing.lin@newcastle.edu.au 6 Department of Mathematics, The University of Newcastle, NSW 2308, Australia. oudone.phanalasy@gmail.com or oudone.phanalasy@newcastle.edu.au 7 Sch...
This paper deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and the labels of the vertices and edges surrounding that face add up to a weight of that face, and the... more
This paper deals with the problem of labeling the vertices, edges and faces of a plane graph in such a way that the label of a face and the labels of the vertices and edges surrounding that face add up to a weight of that face, and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s that appears in the graph. The paper examines the existence of such labelings for disjoint union of plane graphs.
This paper deals with the problem of labeling the vertices, edges and faces of a plane graph. A weight of a face is the sum of the label of a face and the labels of the vertices and edges surrounding that face. In a super d-antimagic... more
This paper deals with the problem of labeling the vertices, edges and faces of a plane graph. A weight of a face is the sum of the label of a face and the labels of the vertices and edges surrounding that face. In a super d-antimagic labeling the vertices receive the smallest labels and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s appearing in the graph. The paper examines the existence of such labelings for plane graphs containing a special Hamilton path.
A graph is called supermagic if it admits a labelling of the edges by pairwise different consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we... more
A graph is called supermagic if it admits a labelling of the edges by pairwise different consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we establish some bounds for the number of edges in supermagic graphs. © 2005 Wiley Periodicals, Inc. J Graph Theory 52: 15–26, 2006