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- G. H. Fath-Tabar
- 2011

In this paper, some bounds for the first and second Zagreb indices of graphs are presented. A new graph invariant, named third Zagreb index, is introduced. Some mathematical properties of this new graph invariant are also presented.

Suppose µ1, µ2, ... , µn are Laplacian eigenvalues of a graph G. The Laplacian energy of G is defined as LE(G) = n i=1 |µ i − 2m/n|. In this paper, some new bounds for the Laplacian eigenvalues and Laplacian energy of some special types of the subgraphs of Kn are presented.

The distance d(u, v) between two vertices u and v of a graph G is equal to the length of a shortest path that connects u and v. Define W W (G, x) = 1/2 {a,b}⊆V (G) x d(a,b)+d 2 (a,b) , where d(G) is the greatest distance between any two vertices. In this paper the hyper-Wiener polynomials of the Cartesian product, composition, join and disjunction of graphs… (More)

For a graph G, Albertson [1] has defined the irregularity of G as irr(G) = xy∈E(G) |d G (x) − d G (y)| where d G (u) is the degree of vertex u. Recently, this graph invariant gained interest in chemical graph theory. In this work, we present some new results on the second minimum of the irregularity of graphs.

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