摘要
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.
图G的P_(k)-路图P_(k)(G)是以G的k-长路构成的集合为点集,这两个路在P_(k)(G)中相邻当且仅当这两个k-长路在G中的交为一个k-1-长路且并未一个k+1-长路或者k-长圈时.令Ek={(v,p):p∈V(P_(k)(G)),v是图P_(k)(G)的一个顶点},定义全P_(k)-图T_(k)(G)如下:T_(k)(G)=(V(G)∪V(P_(k)(G)),E(G)∪E(P_(k)(G))∪Ek).该文研究全P_(k)-图的边连通性.
作者
HAO Chen
TAN Li
ZHUANG Wei
郝琛;谭丽;庄蔚(山西大学,山西太原030006;晋中职业技术学院,山西晋中030600;广西师范学院数学科学学院,广西南宁530023;厦门理工学院数学系,福建厦门361024)
出处
《广西师范学院学报(自然科学版)》
2013年第3期8-12,共5页
Journal of Guangxi Teachers Education University(Natural Science Edition)
基金
supported by Natural Sciences Foundation of Guangxi Province(2012GXNSFBA053005)
