Let G be a simple graph and f be a proper total kcoloring of G. The color set of each vertex v of G is the set of colors appearing on v and the edges incident to v. The coloring f is said to be an adjacent vertex-dist...Let G be a simple graph and f be a proper total kcoloring of G. The color set of each vertex v of G is the set of colors appearing on v and the edges incident to v. The coloring f is said to be an adjacent vertex-distinguishing total coloring if the color sets of any two adjacent vertices are distinct. The minimum k for which such a coloring of G exists is called the adjacent vertex-distinguishing total chromatic number of G. The join graph of two vertex-disjoint graphs is the graph union of these two graphs together with all the edges that connect the vertices of one graph with the vertices of the other. The adjacent vertex-distinguishing total chromatic numbers of the join graphs of an empty graph of order s and a complete graph of order t are determined.展开更多
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), i...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 x^e_(at) (G). In this paper, the adjacent vertexdistinguishing E-total colorings of some join graphs C_m∨G_n are obtained, where G_n is one of a star S_n , a fan F_n , a wheel W_n and a complete graph K_n . As a consequence, the adjacent vertex-distinguishing E-total chromatic numbers of C_m∨G_n are confirmed.展开更多
An adjacent vertex distinguishing incidence coloring of graph G is an incidence coloring of G such that no pair of adjacent vertices meets the same set of colors.We obtain the adjacent vertex distinguishing incidence ...An adjacent vertex distinguishing incidence coloring of graph G is an incidence coloring of G such that no pair of adjacent vertices meets the same set of colors.We obtain the adjacent vertex distinguishing incidence chromatic number of the Cartesian product of a path and a path,a path and a wheel,a path and a fan,and a path and a star.展开更多
基金The Fundamental Research Funds for the Central Universities of China(No.3207013904)
文摘Let G be a simple graph and f be a proper total kcoloring of G. The color set of each vertex v of G is the set of colors appearing on v and the edges incident to v. The coloring f is said to be an adjacent vertex-distinguishing total coloring if the color sets of any two adjacent vertices are distinct. The minimum k for which such a coloring of G exists is called the adjacent vertex-distinguishing total chromatic number of G. The join graph of two vertex-disjoint graphs is the graph union of these two graphs together with all the edges that connect the vertices of one graph with the vertices of the other. The adjacent vertex-distinguishing total chromatic numbers of the join graphs of an empty graph of order s and a complete graph of order t are determined.
基金Supported by the NNSF of China(10771091)Supported by the Qinglan Project of Lianyungang Teacher’s College(2009QLD3)
文摘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 x^e_(at) (G). In this paper, the adjacent vertexdistinguishing E-total colorings of some join graphs C_m∨G_n are obtained, where G_n is one of a star S_n , a fan F_n , a wheel W_n and a complete graph K_n . As a consequence, the adjacent vertex-distinguishing E-total chromatic numbers of C_m∨G_n are confirmed.
基金Supported by the State Ethnic Affairs Commission of China (Grant No. 08XB07)
文摘An adjacent vertex distinguishing incidence coloring of graph G is an incidence coloring of G such that no pair of adjacent vertices meets the same set of colors.We obtain the adjacent vertex distinguishing incidence chromatic number of the Cartesian product of a path and a path,a path and a wheel,a path and a fan,and a path and a star.
