Abstract
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.
Keywords
Irregular graphsHighly irregular graphsNeighbourly irregular graphsPairable verticesNeighbourhood Highly Irregular graphsSupport neighbourly irregular graphs