Eccentric Digraph of Cocktail Party Graph and Hypercube

Tri Atmojo Kusmayadi, Nugroho Arif Sudibyo

Abstract


Let G be a graph with a set of vertices V(G) and a set of edges E(G). The distance from vertex u to vertex v in G, denoted by d(u, v), is the length of the shortest path from vertex u to v. The eccentricity of vertex u in graph G is the maximum distance from vertex u to any other vertices in G, denoted by e(u). Vertex v is an eccentric vertex from u if d(u, v) = e(u). The eccentric digraph ED(G) of a graph G is a graph that has the same set of vertices as G, and there is an arc (directed edge) joining vertex u to v if v is an eccentric vertex from u. In this paper, we determine the eccentric digraph of a class of graph called the cocktail party graph and hypercube.

Keywords


cocktail party graph; eccentric digraph; eccentricity; hypercube

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References


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DOI: http://dx.doi.org/10.12962/j20882033.v22i4.74

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