# The order difference interval graph of a group

Document Type: Research Paper

Authors

1 Department of Mathematics, Manonmaniam Sundaranar University, tirunelveli

2 Department of Mathematics Manonmaniam Sundaranar University Tirunelveli 627 012, Tamil Nadu, India.

Abstract

‎‎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.

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### References

T. M. Apostol (1998). Introduction to Analytic number theory. Narosa Publishing house, New Delhi.