On the Relationships between THE HYPER-ZAGREB INDEX AND GRAPH Eigenvalues

Let G be a simple connected graph. The first and second Zagreb indices have been introduced as: where deg(u) is the degree of vertex (u) . The hyper-Zagreb index of a connected graph G, denoted by HM(G), is defined as : where deg(u) is the degree of a vertex u in G. In this paper,we study the graphs eigenvalues and we define a new bound on Hyper Zagreb index.

Keywords:

Degree , Zagreb index , hyper-Zagreb index , eigenvalues , adjacency matrix , Characteristic polynomial