Injective chromatic number of lexicographic product of two graphs
نویسندگان
چکیده
منابع مشابه
On the injective chromatic number of graphs
We define the concepts of an injective colouring and the injective chromatic number of a graph and give some upper and lower bounds in general, plus some exact values. We explore in particular the injective chromatic number of the hypercube and put it in the context of previous work on similar concepts, especially the theory of errorcorrecting codes. Finally, we give necessary and sufficient co...
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The injective chromatic number χi(G) [5] of a graph G is the minimum number of colors needed to color the vertices of G such that two vertices with a common neighbor are assigned distinct colors. In this paper we define injective chromatic sum and injective strength of a graph and obtain the injective chromatic sum of complete graph, paths, cycles, wheel graph and complete bipartite graph. We a...
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We give some bounds on the injective chromatic number. © 2009 Elsevier B.V. All rights reserved.
متن کاملImproved Bounds for the Chromatic Number of the Lexicographic Product of Graphs
An upper bound for the chromatic number of the lexicographic product of graphs which unifies and generalizes several known results is proved. It is applied in particular to characterize graphs that have a complete core. An improved lower bound is also given.
متن کاملOn the chromatic number of the lexicographic product and the Cartesian sum of graphs
Let G[H] be the lexicographic product of graphs G and H and let G⊕H be their Cartesian sum. It is proved that if G is a nonbipartite graph, then for any graph H, χ(G[H]) ≥ 2χ(H)+d k e, where 2k+1 is the length of a shortest odd cycle of G. Chromatic numbers of the Cartesian sum of graphs are also considered. It is shown in particular that for χ–critical and not complete graphs G and H, χ(G ⊕ H)...
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ژورنال
عنوان ژورنال: Malaya Journal of Matematik
سال: 2019
ISSN: 2319-3786,2321-5666
DOI: 10.26637/mjm0s01/0085