Concise proofs for adjacent vertex-distinguishing total colorings

38Citations
Citations of this article
6Readers
Mendeley users who have this article in their library.

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 χa t (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 χa t (G) when G is a complete graph or a cycle. © 2008 Elsevier B.V. All rights reserved.

Cite

CITATION STYLE

APA

Hulgan, J. (2009). Concise proofs for adjacent vertex-distinguishing total colorings. Discrete Mathematics, 309(8), 2548–2550. https://doi.org/10.1016/j.disc.2008.06.002

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free