THE ECCENTRIC DIGRAPH OF THE CORONA OF Cn WITH Km, Cm OR Pm
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 ofthe 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. Inthis
paper, we answer the open problem proposed by Boland and Miller [1] to find the
eccentric digraph of various classes of graphs. In particular, we determine the
eccentric digraph of the corona of Cn with Km; Cm and Pm, with Cn; Km or Pmare
cycle, complete graph and path, respectively.
Author: Sri Kuntari and Tri
Atmojo Kusmayadi
Journal Code: jpmatematikagg120015
