摘要： Let G(V, E) be a simple connected graph and k be positive integers. A mapping f from V∪E to {1, 2, ··· , k} is called an adjacent vertex-distinguishing E-total coloring of G(abbreviated to k-AVDETC), if for uv ∈ E(G), we have f(u) ≠ f(v), f(u) ≠ f(uv), f(v) ≠ f(uv), C(u) ≠C(v), where C(u) = {f(u)}∪{f(uv)|uv ∈ E(G)}. The least number of k colors required for which G admits a k-coloring is called the adjacent vertex-distinguishing E-total chromatic number of G is denoted by xeat(G). In this paper, the adjacent vertexdistinguishing E-total colorings of some join graphs Cm∨Gn are obtained, where Gn is one of a star Sn, a fan Fn , a wheel Wn and a complete graph Kn. As a consequence, the adjacent vertex-distinguishing E-total chromatic numbers of Cm∨Gn are confirmed.
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