ON THE STABILITY OF COMMON NEIGHBOR POLYNOMIAL OF SOME GRAPHS

Let G(V,E) be a simple graph of order n with vertex set V and edge set E. Let (u, v) denotes an unordered vertex pair of distinct vertices of G. The i-common neighbor set of G is dened as N(G, i) := {(u; v) : u; v ∈ V; u ≠ v and |N(u) ∩ N(v)| = i}, for 0 ≤ i ≤ n-2. The polynomial N[G; x] = ∑_i=0^(n-2) |N(G; i)|xⁱ is defined as the common neighbor polynomial of G. A root of the polynomial N[G; x] is defined as the common neighbor root of the graph G. In this paper we study the stability of common neighbor polynomial of some graphs.