%0 Journal Article
%T The order difference interval graph of a group
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Balakrishnan, P.
%A Kala, R.
%D 2012
%\ 06/01/2012
%V 1
%N 2
%P 59-65
%! The order difference interval graph of a group
%K Order difference interval graph
%K unicyclic graph
%K Eulerian
%K gen-
erating set
%R 10.22108/toc.2012.1588
%X In this paper we introduce the concept of order difference interval graph $\Gamma_{ODI}(G)$ of a group $G$. It is a graph $\Gamma_{ODI}(G)$ with $V(\Gamma_{ODI}(G)) = G$ and two vertices $a$ and $b$ are adjacent in $\Gamma_{ODI}(G)$ if and only if $o(b)-o(a) \in [o(a), o(b)]$. Without loss of generality, we assume that $o(a) \leq o(b)$. In this paper we obtain several properties of $\Gamma_{ODI}(G)$, upper bounds on the number of edges of $\Gamma_{ODI}(G)$ and determine those groups whose order difference interval graph is isomorphic to a complete multipartite graph.
%U https://toc.ui.ac.ir/article_1588_9fb8176991b10ac13f1c1c7d632dd893.pdf