Semi Neighbourly Irregular Graphs

A connected graph G is said to be semi neighbourly irregular (SNI) if no two adjacent vertices of G have the same number of vertices ata distance two away from them. That is, d2(u) 6= d2(v), for every edge uv in E(G), (where d2(v) is defined as the number of vertices at a distance 2away from v). This paper suggests a method to construct semi neighbourly irregular graphs which contain every graph of order n ≥ 2 as an inducedsubgraph. We have also defined strict semi neighbourly irregular tree and semi neighbourly regular strength of a graph. We also study few propertiespossessed by semi neighbourly irregular graphs and semi neighbourly irregular trees