Abstract
A graph G is said to be non-neighbour irregular graph if no two nonadjacent vertices of G have same degree. This paper suggests the methods of construction of non-neighbour irregular graphs. This paper also includes a few properties possessed by these non-neighbour irregular graphs.
Highlights
Throughout this paper we consider only undirected, finite and simple graphs
This paper suggests the methods of construction of non-neighbour irregular graphs
This paper includes a few properties possessed by these non-neighbour irregular graphs
Summary
Throughout this paper we consider only undirected, finite and simple graphs. Let G be such graph with vertex set V (G). Perhaps one of the first graph transformation of a graph G is its complement denoted by G , which is a graph with vertex set V(G) in which two vertices are adjacent if and only if they are nonadjacent in G and dG (v) = n 1 dG (v) holds for all v V (G) , where n is the number of vertices of G. A connected graph G is said to be a k-neighbourhood regular graph if each of its vertices is adjacent to exactly k -vertices of the same degree. A connected graph G is said to be neighbourly irregular graph abbreviated as NI graph if no two adjacent vertices of G have the same degree Inspired by these three definitions we define the concept of non-neighbour irregular graphs abbreviated as NNI graphs
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