A vertex distinguishing edge coloring of a graph G is a proper edge coloring of G such that any pair of vertices has the distinct sets of colors. The minimum number of colors required for a vertex distinguishing edge ...A vertex distinguishing edge coloring of a graph G is a proper edge coloring of G such that any pair of vertices has the distinct sets of colors. The minimum number of colors required for a vertex distinguishing edge coloring of a graph C is denoted by Xs＇8（G）. In this paper, we obtained upper bounds on the vertex distinguishing chromatic index of 3-regular Halin graphs and Halin graphs with △（G） ≥ 4, respectively.展开更多
For any graph?G,?G?together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number?k(G)?of a graph?G?is defined to be the smallest number of such isolated ver...For any graph?G,?G?together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number?k(G)?of a graph?G?is defined to be the smallest number of such isolated vertices. In general, it is hard to compute the competition number?k(G)?for a graph?G?and chara-cterizing a graph by its competition number has been one of important research problems in the study of competition graphs. A 2-connected planar graph?G?with minimum degree at least 3 is a pseudo-Halin graph if deleting the edges on the boundary of a single face?f0?yields a tree. It is a Halin graph if the vertices of?f0?all have degree 3 in?G. In this paper, we compute the competition numbers of a kind of pseudo-Halin graphs.展开更多
Let G be a planar graph with δ(G)≥3, fo be a face of G. In this paper it is proved that for any Halin graph with △(G)≥6, X (G)＝△(G)+1, where △(G), Xo (G) denote the maximum degree and the complete chromatic num...Let G be a planar graph with δ(G)≥3, fo be a face of G. In this paper it is proved that for any Halin graph with △(G)≥6, X (G)＝△(G)+1, where △(G), Xo (G) denote the maximum degree and the complete chromatic number of G, respectively.展开更多
基金Supported by the National Natural Science Foundation of China(10971198)the Zhejiang Natural Science Foundation of China(Z6110786)
文摘A vertex distinguishing edge coloring of a graph G is a proper edge coloring of G such that any pair of vertices has the distinct sets of colors. The minimum number of colors required for a vertex distinguishing edge coloring of a graph C is denoted by Xs＇8（G）. In this paper, we obtained upper bounds on the vertex distinguishing chromatic index of 3-regular Halin graphs and Halin graphs with △（G） ≥ 4, respectively.
文摘For any graph?G,?G?together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number?k(G)?of a graph?G?is defined to be the smallest number of such isolated vertices. In general, it is hard to compute the competition number?k(G)?for a graph?G?and chara-cterizing a graph by its competition number has been one of important research problems in the study of competition graphs. A 2-connected planar graph?G?with minimum degree at least 3 is a pseudo-Halin graph if deleting the edges on the boundary of a single face?f0?yields a tree. It is a Halin graph if the vertices of?f0?all have degree 3 in?G. In this paper, we compute the competition numbers of a kind of pseudo-Halin graphs.
文摘Let G be a planar graph with δ(G)≥3, fo be a face of G. In this paper it is proved that for any Halin graph with △(G)≥6, X (G)＝△(G)+1, where △(G), Xo (G) denote the maximum degree and the complete chromatic number of G, respectively.
