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.
Highlights
Many classes of graphs like hypercubes, Hamming graphs, prisms, etc. which find enormous applications in wide variety of fields like natural and social sciences, computer science, engineering, etc. are graph products themselves or are closely related to them
Cartesian product has been widely used by graph theorists and others too
A monograph by Imrich et al [4] on graphs and their cartesian products reiterate the importance of the concept
Summary
Many classes of graphs like hypercubes, Hamming graphs, prisms, etc. which find enormous applications in wide variety of fields like natural and social sciences, computer science, engineering, etc. are graph products themselves or are closely related to them. The study of these graphs is interesting One such concept, the eccentric digraphs is considered in this article for the product of graphs. The concept of eccentric digraphs of graphs was introduced more than a decade ago by Buckley [7]. It was generalized for digraphs by Boland and Miller [8]. Buckley [7] defined the eccentric digraph ED(G) of a graph G as having the same vertex set as G and there is an arc from u to v if v is an eccentric vertex of u.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
