• ON EDGE-EDGE DOMINATION IN GRAPHS

D. K. THAKKAR, N. P. JAMVECHA*

Abstract


In this paper we further study the concept of edge-edge domination in graphs. We observe that the edge-edge domination number of a graph may increase or decrease or remains same when a edge is removed from a graph. We proved a necessary and sufficient condition under which the edge-edge domination number of a graph increases and also we proved a necessary and sufficient condition under which the edge-edge domination number of a graph decreases. For this purpose we introduce two new concepts namely e-dominating neighbourhood of an edge and private edge-edge neighbourhood of an edge with respect to a set containing the edge. Some examples also have been given.


Keywords


edge-edge dominating set, minimal edge-edge dominating set, minimum edge-edge dominating set, edge-edge domination number, e-dominating neighbourhood, Private edge-edge neighbourhood.

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