A total-coloring of a graph G is strict neighbor-distinguishing if for any two adjacent vertices u and v,the set of colors used on u and its incident edges and the set of colors used on v and its incident edges are no...A total-coloring of a graph G is strict neighbor-distinguishing if for any two adjacent vertices u and v,the set of colors used on u and its incident edges and the set of colors used on v and its incident edges are not included with each other.The strict neighbor-distinguishing total indexχ"_(snd)(G)of G is the minimum number of colors in a strict neighbor-distinguishing total-coloring of G.In this paper,we prove that every simple graph G withΔ(G)≥3 satisfiesχ"_(snd)(G)≤2Δ(G).展开更多
基金NSFC(Grant Nos.11771402,12031018,12071048)Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000)。
文摘A total-coloring of a graph G is strict neighbor-distinguishing if for any two adjacent vertices u and v,the set of colors used on u and its incident edges and the set of colors used on v and its incident edges are not included with each other.The strict neighbor-distinguishing total indexχ"_(snd)(G)of G is the minimum number of colors in a strict neighbor-distinguishing total-coloring of G.In this paper,we prove that every simple graph G withΔ(G)≥3 satisfiesχ"_(snd)(G)≤2Δ(G).
