Support Neighbourly Irregular Graphs

A new family of irregular graphs namely support neighbourly irregular graph has been introduced and studied for its properties in this paper. In any graph, the support of a vertex is the sum of degrees of its neighbours. A connected graph G is said to be support neighbourly irregular (or simply SNI), if no two adjacent vertices in G have same support. A necessary and sufficient condition for a graph to be SNI has been established and the relationship of SNI graphs with other family irregular graphs have been discussed in this paper.