A Study on Ornated Graphs

Abstract

In this paper, we introduce the notion of a finite non-simple directed graph, called an ornated graph and initiate a study on ornated graphs. An ornated graph is a directed graph on $n$ vertices, denoted by $O_n(s_l)$, whose vertices are consecutively labeled clockwise on the circumference of a circle and constructed from an ordered string $s_l$ joining them in such a way that for an odd indexed entry $a_t$ of the string, a tail $v_i$ has clockwise heads $v_j$ if and only if $(i+a_t) \ge j$ and for an even indexed entry $a_s$ of the string a tail $v_i$ has anticlockwise heads $v_j$ if and only if $(i-a_s) \le j$. The collection of the ornated graphs having this property is called the family of ornated graphs. Some interesting results are also presented in this paper on certain types of ornated graphs.