Total coloring conjecture for vertex, edge and neighborhood corona products of graphs
2019 ◽
Vol 11
(01)
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pp. 1950014
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A total coloring of a graph [Formula: see text] is an assignment of colors to the elements of the graph [Formula: see text] such that no adjacent vertices and edges receive the same color. The total chromatic number of a graph [Formula: see text], denoted by [Formula: see text], is the minimum number of colors that suffice in a total coloring. Behzad and Vizing conjectured that for any simple graph [Formula: see text], [Formula: see text], where [Formula: see text] is the maximum degree of [Formula: see text]. In this paper, we prove the tight bound of the total coloring conjecture for the three types of corona products (vertex, edge and neighborhood) of graphs.
2018 ◽
Vol 10
(02)
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pp. 1850018
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2011 ◽
Vol 474-476
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pp. 2341-2345
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2013 ◽
Vol 475-476
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pp. 379-382
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1992 ◽
Vol 53
(2)
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pp. 219-228
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2011 ◽
Vol 225-226
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pp. 243-246
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