On the b-chromatic number of some graph products
2012 ◽
Vol 49
(2)
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pp. 156-169
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Keyword(s):
A b-coloring is a proper vertex coloring of a graph such that each color class contains a vertex that has a neighbor in all other color classes and the b-chromatic number is the largest integer φ(G) for which a graph has a b-coloring with φ(G) colors. We determine some upper and lower bounds for the b-chromatic number of the strong product G ⊠ H, the lexicographic product G[H] and the direct product G × H and give some exact values for products of paths, cycles, stars, and complete bipartite graphs. We also show that the b-chromatic number of Pn ⊠ H, Cn ⊠ H, Pn[H], Cn[H], and Km,n[H] can be determined for an arbitrary graph H, when integers m and n are large enough.
2020 ◽
Vol 12
(02)
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pp. 2050021
Keyword(s):
2013 ◽
Vol Vol. 15 no. 1
(Graph Theory)
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2015 ◽
Vol 9
(1)
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pp. 39-58
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2018 ◽
Vol 7
(4.10)
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pp. 393
2018 ◽
Vol 2
(1)
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pp. 30
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