Distance-edge-monitoring numbers of some related pseudo wheel networks
Chenxu Yang, Xingchao Deng, Zhen Ji, Wen Li · International Journal of Parallel Emergent and Distributed Systems · 2024
For a set M of vertices and an edge e of a graph G, let PG(M,e) be the set of the pair (x,y) with a vertex x of M and a vertex y of V(G) such that dG(x,y)≠dG−e(x,y). For a vertex x, let EM(x) be the edge set e such that there exists a vertex v in G with (x,v)∈P({x},e). A set M of vertices of a graph G is distance-edge-monitoring set if every edge e of G is monitored by some vertex v∈M, that is, for any e∈E(G), we have PG(M,e)≠∅. The distance-edge-monitoring number of a graph G, denoted by dem(G), is defined as the smallest size of distance-edge-monitoring sets of G. In this paper, we study the distance edge monitoring number of pseudo wheel graphs, that is, some variants of wheel graph.