Add to ORKGThe square G2 of a graph G is defined on the vertex set of G in such a way that distinct vertices with distance at most two in G are joined by an edge. We study the chromatic number of the square of the Cartesian product Cm2Cn of two cycles and show that the value of this parameter is at most 7 except when m = n = 3, in which case the value is 9, and when m = n = 4 or m = 3 and n = 5, in which case the value is 8. Moreover, we conjecture that for every G = Cm2Cn, the chromatic number of G2 equals ⌈mn/α(G2)⌉, where α(G2) denotes the size of a maximal independent set in G2
AbstractLet G[H] be the lexicographic product of graphs G and H and let G ⊕ H be their Cartesian sum...
The square G2 of a graph G is the graph defined on V (G) such that two vertices u and v are adjacent...
AbstractA labeling of a graph G is distinguishing if it is only preserved by the trivial automorphis...
The square G2 of a graph G is defined on the vertex set of G in such a way that distinct vertices wi...
AbstractThe square G2 of a graph G is defined on the vertex set of G in such a way that distinct ver...
Abstract. A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which ...
The square ▫$G^2$▫ of a graph ▫$G$▫ is obtained from ▫$G$▫ by adding edges joining all pairs of node...
A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two verti...
We prove upper and lower bounds on the chromatic number of the square of the cartesian product of tr...
AbstractThe chromatic difference sequence cds(G) of a graph G with chromatic number n is defined by ...
AbstractFor graphs G and H, let G⊕H denote their Cartesian sum. We investigate the chromatic number ...
LetCm bethecycleof length m. WedenotetheCartesian productof ncopies of Cm by G(n,m): = Cm□Cm□···□Cm....
AbstractLet Cm be the cycle of length m. We denote the Cartesian product of n copies of Cm by G(n,m)...
Abstract. The game chromatic number χg is considered for the Cartesian product G2H of two graphs G a...
For graphs G and H, let G ⊕ H denote their Cartesian sum. We investigate the chromatic number and th...
AbstractLet G[H] be the lexicographic product of graphs G and H and let G ⊕ H be their Cartesian sum...
The square G2 of a graph G is the graph defined on V (G) such that two vertices u and v are adjacent...
AbstractA labeling of a graph G is distinguishing if it is only preserved by the trivial automorphis...
The square G2 of a graph G is defined on the vertex set of G in such a way that distinct vertices wi...
AbstractThe square G2 of a graph G is defined on the vertex set of G in such a way that distinct ver...
Abstract. A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which ...
The square ▫$G^2$▫ of a graph ▫$G$▫ is obtained from ▫$G$▫ by adding edges joining all pairs of node...
A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two verti...
We prove upper and lower bounds on the chromatic number of the square of the cartesian product of tr...
AbstractThe chromatic difference sequence cds(G) of a graph G with chromatic number n is defined by ...
AbstractFor graphs G and H, let G⊕H denote their Cartesian sum. We investigate the chromatic number ...
LetCm bethecycleof length m. WedenotetheCartesian productof ncopies of Cm by G(n,m): = Cm□Cm□···□Cm....
AbstractLet Cm be the cycle of length m. We denote the Cartesian product of n copies of Cm by G(n,m)...
Abstract. The game chromatic number χg is considered for the Cartesian product G2H of two graphs G a...
For graphs G and H, let G ⊕ H denote their Cartesian sum. We investigate the chromatic number and th...
AbstractLet G[H] be the lexicographic product of graphs G and H and let G ⊕ H be their Cartesian sum...
The square G2 of a graph G is the graph defined on V (G) such that two vertices u and v are adjacent...
AbstractA labeling of a graph G is distinguishing if it is only preserved by the trivial automorphis...