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.
T. M. Apostol (1998). Introduction to Analytic number theory. Narosa Publishing house, New Delhi. F. Harary (1969). Graph Theory. Addison-Wesley, Reading, Mass. I. N. Herstein (2003). Topics in Algebra. Second edition, John Wiley \& Sons. M. Sattanathan and R. Kala (2009). An Introduction to Order Prime Graph. nt. J. Contemp. Math. Sci.. 4 (10), 467-474
Balakrishnan, P., & Kala, R. (2012). The order difference interval graph of a group. Transactions on Combinatorics, 1(2), 59-65. doi: 10.22108/toc.2012.1588
MLA
P. Balakrishnan; R. Kala. "The order difference interval graph of a group". Transactions on Combinatorics, 1, 2, 2012, 59-65. doi: 10.22108/toc.2012.1588
HARVARD
Balakrishnan, P., Kala, R. (2012). 'The order difference interval graph of a group', Transactions on Combinatorics, 1(2), pp. 59-65. doi: 10.22108/toc.2012.1588
VANCOUVER
Balakrishnan, P., Kala, R. The order difference interval graph of a group. Transactions on Combinatorics, 2012; 1(2): 59-65. doi: 10.22108/toc.2012.1588
)
