Frontiers of Mathematics in China >
Neighbor sum distinguishing total chromatic number of K4-minor free graph
Received date: 30 Oct 2015
Accepted date: 23 Apr 2017
Published date: 06 Jul 2017
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A k-total coloring of a graph G is a mapping φ: V (G) ∪ E(G) →{1, 2, . . . , k} such that no two adjacent or incident elements in V (G) ∪ E(G) receive the same color. Let f(v) denote the sum of the color on the vertex v and the colors on all edges incident with v. We say that φ is a k-neighbor sum distinguishing total coloring of G if f(u) ≠ f(v) for each edge uv ∈ E(G). Denote the smallest value k in such a coloring of G. Pilśniak andWoźniak conjectured that for any simple graph with maximum degree Δ(G), . In this paper, by using the famous Combinatorial Nullstellensatz, we prove that for K4-minor free graph G with Δ(G)≥5, if G contains no two adjacent Δ-vertices, otherwise, .
Hongjie SONG , Changqing XU . Neighbor sum distinguishing total chromatic number of K4-minor free graph[J]. Frontiers of Mathematics in China, 2017 , 12(4) : 937 -947 . DOI: 10.1007/s11464-017-0649-9
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