大连理工大学学报2017，Vol.57Issue(4)：430-435,6.DOI:10.7511/dllgxb201704015
圈与路联图点可区别Ⅰ-全染色和点可区别Ⅵ-全染色
Vertex-distinguishing Ⅰ-total colorings and vertex-distinguishing Ⅵ-total colorings of join-graph of cycle and path
摘要
Abstract
Ⅰ-total coloring of a graph G is an assignment of several colors to the vertices and edges of graph G such that any two adjacent vertices receive different colors and any two adjacent edges receive different colors.Ⅵ-total coloring of a graph G is an assignment of several colors to the vertices and edges of graph G such that any two adjacent edges receive different colors.For Ⅰ(Ⅵ)-total coloring of graph G and a vertex x of graph G,C(x)is used to denote the set (not multiset)composed of color of x and colors of the edges incident with x .Let f be Ⅰ(Ⅵ)-total coloring of a graph G using k colors and C (u )≠C (v )for any two different vertices u and v of graph G,then f is called a k-vertex-distinguishing Ⅰ(Ⅵ)-total coloring of graph G,or k-VDITC (VDVITC)of graph G for short.The minimum number of colors required in a VDITC (VDVITC)is the vertex-distinguishing Ⅰ(Ⅵ)-total chromatic number.The problems of vertex-distinguishing Ⅰ (Ⅵ)-total colorings of the join-graph Cm ∨P n of cycle and path are discussed by the method of combinatorial analysis and constructing concrete coloring.Meanwhile,vertex-distinguishing Ⅰ(Ⅵ)-total chromatic numbers of graph Cm ∨P n are determined.The results illustrate that the VDITC conjecture and VDVITC conjecture are valid for graph Cm ∨P n .关键词
Ⅰ-全染色/点可区别Ⅰ-全染色/点可区别Ⅰ-全色数/圈与路的联Key words
Ⅰ-total coloring/vertex-distinguishing Ⅰ-total coloring/vertex-distinguishing Ⅰ-total chromatic number/join of cycle and path分类
数理科学引用本文复制引用
苗婷婷,王治文,陈祥恩..圈与路联图点可区别Ⅰ-全染色和点可区别Ⅵ-全染色[J].大连理工大学学报,2017,57(4):430-435,6.基金项目
国家自然科学基金资助项目(61163037,61163054,11261046,61363060) （61163037,61163054,11261046,61363060）
宁夏回族自治区百人计划资助项目. （）
