Abstract
In this paper, we introduce a new family of irregular graphs called support neighbourly edge irregular graphs based on degree in edge sense. In any graph, the support of an edge is the sum of the edge degrees of its neighbours. A graph is said to be support neighbourly edge irregular(or simply SNEI), if any two adjacent edges have different support. Basic properties of theses graphs are studied. A necessary and sufficient condition for a graph to be SNEI has been obtained and several methods to construct SNEI graph from other graphs have been discussed. Key words: Neighbourly irregular graphs, Neighbourly edge irregular fuzzy graphs, support neighbourly irregular graphs, Support neighbourly edge irregular graphs.
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