A Study on Ornated Graphs

Abstract

In this paper, we introduce the notion of a finite non-simple directed graph called, an ornated graph. An ornated graph is a directed graph on [Formula: see text] vertices, denoted by [Formula: see text], whose vertices are consecutively labeled clockwise on the circumference of a circle and constructed from an ordered string [Formula: see text]. Joining vertices is such that for an odd indexed entry [Formula: see text] of the string, a tail vertex [Formula: see text] has clockwise heads [Formula: see text] if and only if [Formula: see text]. For an even indexed entry [Formula: see text] of the string, a tail vertex [Formula: see text] has anticlockwise heads [Formula: see text] if and only if [Formula: see text]. Some interesting results for certain types of ornated graphs are presented.