EDGE METRIC DIMENSION OF k MULTIWHEEL GRAPH

摘要

If we consider G = (V, E) to be a connected graph, with v is an element of V and e = uw is an element of E, then d(G)(e, v) = min{d(G)(u, v), d(G) (w, v)} has been defined as the distance between a vertex v and an edge e. The cardinality of the smallest subset S subset of V which can assign a unique distance vector to every edge of G is referred to as edge metric dimension (EMD) given by edim(G). A k multiwheel graph W-1,W- n,W- k is composed of k cycles C-n along with a central vertex x such that x is adjacent to each of the vertices of C-1 and the corresponding vertices of the two consecutive cycles C-i and Ci+i are also adjacent for all 1 <= i <= (k - 1). This article discusses the EMD of the double wheel graph and extends the results to the general k multiwheel graph.