摘要:Let G be a simple graph with no isolated edge. An/-total coloring of a graphG is a mapping Ф : V(G) U E(G) → (1, 2,…… , k) such that no adjacent vertices receive thesame color and no adjacent edges receive the same color. An/-total coloring of a graph G issaid to be adjacent vertex distinguishing if for any pair of adjacent vertices u and v of G, wehave CФ(u) ≠ CФ(v), where CФ(u) denotes the set of colors of u and its incident edges. Theminimum number of colors required for an adjacent vertex distinguishing I-total coloring of GG is called the adjacent vertex distinguishing I-total chromatic number, denoted by Xat(G).In this paper, we characterize the adjacent vertex distinguishing I-total chromatic numberof outerplanar graphs.
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