A total coloring of a graph G with colors 1, 2, ..., t is called a cyclically interval total t-coloring if all colors are used, and the edges incident to each vertex v∈V(G) together with v are colored by (dG(v)+1) co...A total coloring of a graph G with colors 1, 2, ..., t is called a cyclically interval total t-coloring if all colors are used, and the edges incident to each vertex v∈V(G) together with v are colored by (dG(v)+1) consecutive colors modulo t, where dG(v) is the degree of the vertex v in G. The one point union ?of k-copies of cycle Cn is the graph obtained by taking v as a common vertex such that any two distinct cycles? and? are edge disjoint and do not have any vertex in common except v. In this paper, we study the cyclically interval total colorings of , where n≥3 and k≥2.展开更多
Let G be a simple graph and f be a proper total coloring(or a total coloring in brief) of G. For any vertex u in G, Cf(u) denote the set of colors of vertex u and edges which incident with vertex u. Cf(u) is said to b...Let G be a simple graph and f be a proper total coloring(or a total coloring in brief) of G. For any vertex u in G, Cf(u) denote the set of colors of vertex u and edges which incident with vertex u. Cf(u) is said to be the color set of vertex u under f. If Cf(u) = Cf(v)for any two distinct vertices u and v of G, then f is called vertex-distinguishing total coloring of G(in brief VDTC), a vertex distinguishing total coloring using k colors is called k-vertexdistinguishing total coloring of G(in brief k-VDTC). The minimum number k for which there exists a k-vertex-distinguishing total coloring of G is called the vertex-distinguishing total chromatic number of G, denoted by χvt(G). By the method of prior distributing the color sets, we obtain vertex-distinguishing total chromatic number of m C9 in this paper.展开更多
文摘A total coloring of a graph G with colors 1, 2, ..., t is called a cyclically interval total t-coloring if all colors are used, and the edges incident to each vertex v∈V(G) together with v are colored by (dG(v)+1) consecutive colors modulo t, where dG(v) is the degree of the vertex v in G. The one point union ?of k-copies of cycle Cn is the graph obtained by taking v as a common vertex such that any two distinct cycles? and? are edge disjoint and do not have any vertex in common except v. In this paper, we study the cyclically interval total colorings of , where n≥3 and k≥2.
基金Supported by the NNSF of China(Grant No.11761064,61163037)
文摘Let G be a simple graph and f be a proper total coloring(or a total coloring in brief) of G. For any vertex u in G, Cf(u) denote the set of colors of vertex u and edges which incident with vertex u. Cf(u) is said to be the color set of vertex u under f. If Cf(u) = Cf(v)for any two distinct vertices u and v of G, then f is called vertex-distinguishing total coloring of G(in brief VDTC), a vertex distinguishing total coloring using k colors is called k-vertexdistinguishing total coloring of G(in brief k-VDTC). The minimum number k for which there exists a k-vertex-distinguishing total coloring of G is called the vertex-distinguishing total chromatic number of G, denoted by χvt(G). By the method of prior distributing the color sets, we obtain vertex-distinguishing total chromatic number of m C9 in this paper.
