Dec 28, 2008 · The Cartesian sum of G and H , denoted by G ⊕ H , has as the vertex set V × V ′ , and the edge set E ( G ⊕ H ) = { ( x , x ′ ) ( y , y ′ ) : x y ...

These results improve previously known bounds on the chromatic number and the circular chromatic number for the Cartesian sum of graphs. Previous article in ...

Jan 6, 2004 · For graphs G and H, let G ⊕ H denote their Cartesian sum. This paper investigates the chromatic number and the circular chromatic number for ...

For graphs G and H, let G circle plus H denote their Cartesian sum. We investigate the chromatic number and the circular chromatic number for G circle plus ...

Form G0 by adding vertices u and s to G, and edges so that u is adjacent to every vertex in A and s is adjacent to every vertex in B. If χ(G0) > k, then G0 ...

For graphs G and H , let G ⊕ H denote their Cartesian sum. We investigate the chromatic number and the circular chromatic number for G ⊕ H . It has been ...

Apr 23, 2023 · The coloring c is called a set coloring if NC(u) 6= NC(v) for every pair of adjacent vertices u and v of G. The minimum number of colors ...

In graph theory, the Cartesian product G □ H of graphs G and H is a graph such that: the vertex set of G □ H is the Cartesian product V(G) × V(H); and ...

For graphs G and H, let G ⊕ H denote their Cartesian sum. We prove that for any graphs G and H, χ ( G ⊕ H ) ⩽ max { ⌈ χ c ( G ) χ ( H ) ⌉ , ⌈ χ ( G ) ...