Products and Eccentric Diagraphs
Medha Itagi Huilgol *
Department of Mathematics, Bangalore University, Central College Campus, BANGALORE - 560 001, India.
Syed Asif Ulla S.
Department of Mathematics, Bangalore University, Central College Campus, BANGALORE - 560 001, India.
*Author to whom correspondence should be addressed.
Abstract
The eccentricity e(u) of a vertex u is the maximum distance of u to any other vertex of G. A vertex v is an eccentric vertex of vertex u if the distance from u to v is equal to e(u). The eccentric digraph ED(G) of a graph(digraph) G is the digraph that has the same vertex as G and an arc from u to v exists in ED(G) if and only if v is an eccentric vertex of u in G. In this paper, we consider the eccentric digraphs of different products of graphs, viz., cartesian, normal, lexicographic, prism, etc.
Keywords: Eccentric vertex, eccentric digraph, cartesian product, lexicographic product, normal product, prism of graphs.