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
In this paper we show that the face-width of any embedding of a Halin graph（a type of planar graph） in the torus is one, and give a formula for determining the number of all nonequivalent embeddings of a Halin graph...In this paper we show that the face-width of any embedding of a Halin graph（a type of planar graph） in the torus is one, and give a formula for determining the number of all nonequivalent embeddings of a Halin graph in the torus.展开更多
Let G be a connected graph having a perfect matching.The graph G is said to be induced matching(IM)extendable if every induced matching M of G is contained in a perfect matching of G.In this paper,we show that Halin g...Let G be a connected graph having a perfect matching.The graph G is said to be induced matching(IM)extendable if every induced matching M of G is contained in a perfect matching of G.In this paper,we show that Halin graph G=T∪C is IM-extendable if and only if its characteristic tree T is isomorphic to K_(1,3),K_(1,5),K_(1,7) or S_(2,2).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
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.
基金Supported by the NNSF of China(10671073)Supported by the NSF of Jiangsu’s Universities( 07KJB110090)
文摘In this paper we show that the face-width of any embedding of a Halin graph（a type of planar graph） in the torus is one, and give a formula for determining the number of all nonequivalent embeddings of a Halin graph in the torus.
基金Supported by the National Natural Science Foundation of China(Grant Nos.61702291,11801371)Key Research Project in Universities of Henan Province(Grant No.21B110004)。
文摘Let G be a connected graph having a perfect matching.The graph G is said to be induced matching(IM)extendable if every induced matching M of G is contained in a perfect matching of G.In this paper,we show that Halin graph G=T∪C is IM-extendable if and only if its characteristic tree T is isomorphic to K_(1,3),K_(1,5),K_(1,7) or S_(2,2).
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.
