The P_(k)-path graph P_(k)(G)corresponding to a graph G has for vertices the set of all paths of length k in G.Two vertices are joined by an edge if and only if the intersection of the corresponding paths forms a path...The P_(k)-path graph P_(k)(G)corresponding to a graph G has for vertices the set of all paths of length k in G.Two vertices are joined by an edge if and only if the intersection of the corresponding paths forms a path of length k-1 in G,and their union forms either a cycle or a path of length k+1.Let Ek={(v,p),p E V(P_(k)(G)),v is an end vertex of p in G},we define total P_(k)-graphs T_(k)(G)as Yk(G)=(V(G)UV(P_(k)(G)),E(G)U E(PI(G))U Ek).In this note,we introduce total P,-graphs Th(G)and study their edge connectivity,as the generaliza-tion of total graphs.展开更多
基金supported by Natural Sciences Foundation of Guangxi Province(2012GXNSFBA053005)
文摘The P_(k)-path graph P_(k)(G)corresponding to a graph G has for vertices the set of all paths of length k in G.Two vertices are joined by an edge if and only if the intersection of the corresponding paths forms a path of length k-1 in G,and their union forms either a cycle or a path of length k+1.Let Ek={(v,p),p E V(P_(k)(G)),v is an end vertex of p in G},we define total P_(k)-graphs T_(k)(G)as Yk(G)=(V(G)UV(P_(k)(G)),E(G)U E(PI(G))U Ek).In this note,we introduce total P,-graphs Th(G)and study their edge connectivity,as the generaliza-tion of total graphs.
