Concise proofs for adjacent vertex-distinguishing total colorings |
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Authors: | Jonathan Hulgan |
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Institution: | Department of Mathematical Sciences, The University of Memphis, Memphis, TN, 38152, USA |
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Abstract: | Let G=(V,E) be a graph and f:(V∪E)→k] be a proper total k-coloring of G. We say that f is an adjacent vertex- distinguishing total coloring if for any two adjacent vertices, the set of colors appearing on the vertex and incident edges are different. We call the smallest k for which such a coloring of G exists the adjacent vertex-distinguishing total chromatic number, and denote it by χat(G). Here we provide short proofs for an upper bound on the adjacent vertex-distinguishing total chromatic number of graphs of maximum degree three, and the exact values of χat(G) when G is a complete graph or a cycle. |
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Keywords: | Adjacent vertex-distinguishing total coloring Adjacent vertex-distinguishing total chromatic number |
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