Graph Products of Open Distance Pattern Uniform Graphs
نویسنده
چکیده
Given an arbitrary non-empty subset M of vertices in a graph G = (V,E), each vertex u in G is associated with the set f o M(u) = {d(u, v) : v ∈ M, u 6= v}, called its open M-distance-pattern. The graph G is called open distancepattern uniform (odpu-) graph if there exists a subset M of V (G) such that f o M(u) = f o M(v) for all u, v ∈ V (G) and M is called an open distance-pattern uniform (odpu-) set of G. The minimum cardinality of an odpu-set in G, if it exists, is called the odpu-number of G and is denoted by od(G). In this paper we characterize several odpu-graphs and constructed classes of odpu-graph products especially, join of two graphs, cartesian product, lexicographic Product and corona.
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