The first and second Zagreb indices of some graph operations

This survey outlines results on graphs extremal with respect to distance–based indices, with emphasis on the Wiener index, hyper–Wiener index, Harary index, Wiener polarity index, reciprocal complementary Wiener index, and terminal Wiener index.

A Survey on Graphs Extremal with Respect to Distance-Based Topological Indices

The Zagreb coindices of graph operations

This article gives a survey of all results on the power graphs of groups and semigroups obtained in the literature. Various conjectures due to other authors, questions and open problems are also included.

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Power graphs: A survey

On the topological index

Vertex and edge PI indices of Cartesian product graphs

We study distance-based graph invariants, such as the Wiener index, the Szeged index, and variants of these two. Relations between the various indices for trees are provided as well as formulas for line graphs and product graphs. This allows us, for instance, to establish formulas for the edge Wiener index of Hamming graphs, C"4-nanotubes and C"4-nanotori. We also determine minimum and maximum of certain indices over the set of all graphs with a given number of vertices or edges. Finally, we study the order of magnitude of the edge Wiener and edge Szeged index, responding negatively to a conjecture that is related to the maximization of the edge Szeged index.

Some new results on distance-based graph invariants

Let G be a graph. The distance d(u,v) between the vertices u and v of the graph G is equal to the length of a shortest path that connects u and v. The Wiener index W(G) is the sum of all distances between vertices of G, whereas the hyper-Wiener index WW(G) is defined as WW(G)=12W(G)[email protected]?"{"u","v"}"@?"V"("G")d(u,v)^2. In this paper the hyper-Wiener indices of the Cartesian product, composition, join and disjunction of graphs are computed. We apply some of our results to compute the hyper-Wiener index of C"4 nanotubes, C"4 nanotori and q-multi-walled polyhex nanotori.

H. Yousefi-Azari

Papers

The first and second Zagreb indices of some graph operations

Vertex and edge PI indices of Cartesian product graphs

Some new results on distance-based graph invariants

The hyper-Wiener index of graph operations

The PI index of product graphs