In a graph G = (V,E), a vertex v âˆˆ V monitors an edge {u, uâ€²} âˆˆ E if {v, u} âˆˆ E and {v, uâ€²} âˆˆ E. Given an n-vertex graph G = (V,E), in which each edge is contained in at least one triangle, and anâ€¦ (More)

Edge monitoring is a simple and effective mechanism for the security of wireless sensor networks. The idea is to award specific roles (monitors) to some sensor nodes of the network. A node v monitorsâ€¦ (More)

In this paper, we study the complexity of the edge monitoring problem. A vertex v monitors an edge e if both extremities together with v form a triangle in the graph. Given a graph G = (V,E) and aâ€¦ (More)

Disclaimer: This is a version of an unedited manuscript that has been accepted for publication. As a service to authors and researchers we are providing this version of the accepted manuscript (AM).â€¦ (More)

Let k be a positive integer, Sk and Ck denote, respectively, a star and a cycle of k edges. Î»Kn is the usual notation for the complete multigraph on n vertices and in which every edge is taken Î»â€¦ (More)