Journal of Discrete Mathematical Sciences and Cryptography, 2021
Abstract In 2013, we [3] introduced the concept of edge pair sum labeling and further studied in ... more Abstract In 2013, we [3] introduced the concept of edge pair sum labeling and further studied in [5-15]. In this paper, we find some new results on edge pair sum labeling.
PRODUCT OF g-VOLTERRA SPACES IN GENERALIZED TOPOLOGICAL SPACES, 2024
In this paper, we introduce the concept of generalized pseudo-base in generalized topological spa... more In this paper, we introduce the concept of generalized pseudo-base in generalized topological spaces, and using this concept, we study the product of g-Volterra space and weakly g-Volterra space in generalized topological spaces. In addition, we study the product of g-Baire space with g-Volterra space in generalized topological spaces.
Graph labeling is currently an emerging area in the research of graph theory. A graph labeling is... more Graph labeling is currently an emerging area in the research of graph theory. A graph labeling is an assignment of integers to vertices or edges or both subject to certain conditions. A detailed survey was done by Gallian in [6]. If the labels of edges are distinct positive integers and for each vertex v the sum of the labels of all edges incident with v is the same for every vertex v in the given graph then the labeling is called a magic labeling.
A simple graph G = (V,E) admits an H-covering if every edge in E belongs to a subgraph of G isomo... 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 be a (p,q )g raph and letf : V (G) →{ 1,2,3, ··· ,p+ q} be an injection. For each edge e = ... more Let G be a (p,q )g raph and letf : V (G) →{ 1,2,3, ··· ,p+ q} be an injection. For each edge e = uv, let f ∗ (e )=( f(u)+f(v))/ 2i ff(u)+f(v )i s even andf ∗ (e )=( f(u)+f(v)+1)/2 if f(u )+ f(v) is odd. Then f is called a super mean labeling if f(V ) ∪{ f ∗ (e ): e ∈ E(G)} = {1,2,3, ··· ,p+q}. A graph that admits a super mean labeling is called a super mean graph. In this paper we present several infinite families of super mean graphs.
Abstract. A vertex irregular total k-labeling of a graph G with vertex setV and edge set E is an ... more Abstract. A vertex irregular total k-labeling of a graph G with vertex setV and edge set E is an assignment of positive integer labels {1,2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted bytvs(G) is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the total vertex irregularity strength of cycle quadrilateral snake, s unflower, double wheel, fungus, triangular book and quadrilateral book.
In this paper we determine the total restrained dominating set and the total restrained dominatio... more In this paper we determine the total restrained dominating set and the total restrained domination subdivision number for Cartesian product graph.
For any non-trivial abelian group A under addition a graph G is said to be A-magic if there exist... more For any non-trivial abelian group A under addition a graph G is said to be A-magic if there exists a labeling f : E(G) ! A − {0} such that, the vertex labeling f+ defined as f+(v) = Pf(uv) taken over all edges uv incident at v is a constant. An A-magic graph G is said to be Zk-magic graph if the group A is Zk, the group of integers modulo k and these graphs are referred as k-magic graphs. In this paper we prove that the graphs such as open star of shell, flower, double wheel, cylinder, wheel, generalised Petersen, lotus inside a circle and closed helm are Zk-magic graphs. Also we prove that super subdivision of any graph is Zk-magic.
Discrete Mathematics, Algorithms and Applications, 2016
For any nontrivial abelian group [Formula: see text] under addition a graph [Formula: see text] i... more For any nontrivial abelian group [Formula: see text] under addition a graph [Formula: see text] is said to be [Formula: see text]-magic if there exists a labeling [Formula: see text] such that the vertex labeling [Formula: see text] defined as [Formula: see text] taken over all edges [Formula: see text] incident at [Formula: see text] is a constant. An [Formula: see text]-magic graph [Formula: see text] is said to be [Formula: see text]-magic graph if the group [Formula: see text] is [Formula: see text] the group of integers modulo [Formula: see text]. These [Formula: see text]-magic graphs are referred to as [Formula: see text]-magic graphs. In this paper, we prove that the graphs such as subdivision of ladder, triangular ladder, shadow, total, flower, generalized prism, [Formula: see text]-snake, lotus inside a circle, square, gear, closed helm and antiprism are [Formula: see text]-magic graphs. Also we prove that if [Formula: see text] be [Formula: see text]-magic graphs with mag...
ABSTRACT A graph G with p vertices and q edges is said to be an odd mean graph if there exists an... more ABSTRACT A graph G with p vertices and q edges is said to be an odd mean graph if there exists an injective function f from the vertex set of G to such that the induced map from the edge set of G to defined by
Journal of Discrete Mathematical Sciences and Cryptography, 2021
Abstract In 2013, we [3] introduced the concept of edge pair sum labeling and further studied in ... more Abstract In 2013, we [3] introduced the concept of edge pair sum labeling and further studied in [5-15]. In this paper, we find some new results on edge pair sum labeling.
PRODUCT OF g-VOLTERRA SPACES IN GENERALIZED TOPOLOGICAL SPACES, 2024
In this paper, we introduce the concept of generalized pseudo-base in generalized topological spa... more In this paper, we introduce the concept of generalized pseudo-base in generalized topological spaces, and using this concept, we study the product of g-Volterra space and weakly g-Volterra space in generalized topological spaces. In addition, we study the product of g-Baire space with g-Volterra space in generalized topological spaces.
Graph labeling is currently an emerging area in the research of graph theory. A graph labeling is... more Graph labeling is currently an emerging area in the research of graph theory. A graph labeling is an assignment of integers to vertices or edges or both subject to certain conditions. A detailed survey was done by Gallian in [6]. If the labels of edges are distinct positive integers and for each vertex v the sum of the labels of all edges incident with v is the same for every vertex v in the given graph then the labeling is called a magic labeling.
A simple graph G = (V,E) admits an H-covering if every edge in E belongs to a subgraph of G isomo... 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 be a (p,q )g raph and letf : V (G) →{ 1,2,3, ··· ,p+ q} be an injection. For each edge e = ... more Let G be a (p,q )g raph and letf : V (G) →{ 1,2,3, ··· ,p+ q} be an injection. For each edge e = uv, let f ∗ (e )=( f(u)+f(v))/ 2i ff(u)+f(v )i s even andf ∗ (e )=( f(u)+f(v)+1)/2 if f(u )+ f(v) is odd. Then f is called a super mean labeling if f(V ) ∪{ f ∗ (e ): e ∈ E(G)} = {1,2,3, ··· ,p+q}. A graph that admits a super mean labeling is called a super mean graph. In this paper we present several infinite families of super mean graphs.
Abstract. A vertex irregular total k-labeling of a graph G with vertex setV and edge set E is an ... more Abstract. A vertex irregular total k-labeling of a graph G with vertex setV and edge set E is an assignment of positive integer labels {1,2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted bytvs(G) is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the total vertex irregularity strength of cycle quadrilateral snake, s unflower, double wheel, fungus, triangular book and quadrilateral book.
In this paper we determine the total restrained dominating set and the total restrained dominatio... more In this paper we determine the total restrained dominating set and the total restrained domination subdivision number for Cartesian product graph.
For any non-trivial abelian group A under addition a graph G is said to be A-magic if there exist... more For any non-trivial abelian group A under addition a graph G is said to be A-magic if there exists a labeling f : E(G) ! A − {0} such that, the vertex labeling f+ defined as f+(v) = Pf(uv) taken over all edges uv incident at v is a constant. An A-magic graph G is said to be Zk-magic graph if the group A is Zk, the group of integers modulo k and these graphs are referred as k-magic graphs. In this paper we prove that the graphs such as open star of shell, flower, double wheel, cylinder, wheel, generalised Petersen, lotus inside a circle and closed helm are Zk-magic graphs. Also we prove that super subdivision of any graph is Zk-magic.
Discrete Mathematics, Algorithms and Applications, 2016
For any nontrivial abelian group [Formula: see text] under addition a graph [Formula: see text] i... more For any nontrivial abelian group [Formula: see text] under addition a graph [Formula: see text] is said to be [Formula: see text]-magic if there exists a labeling [Formula: see text] such that the vertex labeling [Formula: see text] defined as [Formula: see text] taken over all edges [Formula: see text] incident at [Formula: see text] is a constant. An [Formula: see text]-magic graph [Formula: see text] is said to be [Formula: see text]-magic graph if the group [Formula: see text] is [Formula: see text] the group of integers modulo [Formula: see text]. These [Formula: see text]-magic graphs are referred to as [Formula: see text]-magic graphs. In this paper, we prove that the graphs such as subdivision of ladder, triangular ladder, shadow, total, flower, generalized prism, [Formula: see text]-snake, lotus inside a circle, square, gear, closed helm and antiprism are [Formula: see text]-magic graphs. Also we prove that if [Formula: see text] be [Formula: see text]-magic graphs with mag...
ABSTRACT A graph G with p vertices and q edges is said to be an odd mean graph if there exists an... more ABSTRACT A graph G with p vertices and q edges is said to be an odd mean graph if there exists an injective function f from the vertex set of G to such that the induced map from the edge set of G to defined by
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