University of IsfahanTransactions on Combinatorics2251-86571220120601The order difference interval graph of a group5965158810.22108/toc.2012.1588ENP.BalakrishnanDepartment of Mathematics,
Manonmaniam Sundaranar University, tirunelveliR.KalaDepartment of Mathematics
Manonmaniam Sundaranar University
Tirunelveli 627 012, Tamil Nadu, India.Journal Article20120525In 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.https://toc.ui.ac.ir/article_1588_9fb8176991b10ac13f1c1c7d632dd893.pdf