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The order difference interval graph of a group

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Author(s): P. Balakrishnan | R. Kala

Journal: Transactions on Combinatorics
ISSN 2251-8657

Volume: 1;
Issue: 2;
Start page: 59;
Date: 2012;
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Keywords: Order difference interval graph | Unicyclic graph | Eulerian | generating set

ABSTRACT
In this paper we introduce the concept of order difference interval graph ¡ODI (G) of a group G. It is a graph ¡ODI (G) with V (¡ODI (G)) = G and two vertices a and b are adjacent in ¡ODI (G) if and only if o(b) − o(a) ∈ [o(a), o(b)]. Without loss of generality, we assume that o(a) ≤ o(b). In this paper we obtain several properties of ¡ODI (G), upper bounds on the number of edges of ¡ODI (G) and determine those groups whose order difference interval graph is isomorphic to a complete multipartite graph.
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