Title : ( Further Results On the Third Zagreb Index of Graphs )
Authors: Mostafa Tavakoli , Freydoon Rahbarnia , Madjid Mirzavaziri , A. R. Ashrafi ,
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Abstract
Suppose G is a simple graph. The third Zagreb index of G is defined as M3(G) =∑e=uvE(G) |deg(u)-deg(v)|. In this paper, it is proved that the third Zagreb index of a graph is an even non-negative integer. Moreover, any even non-negative integer is the third Zagreb index of a given caterpillar. We also prove that if T is an arbitrary tree then M (T) is not equal to 4. Finally the maximum and minimum of this graph invariant in the classes of Finally the maximum and minimum of this graph invariant in the classes of all tricyclic and tetracyclic graphs are computed.
Keywords
, Tricyclic graph, Tetracyclic graph, Third Zagreb index.
@inproceedings{paperid:1032610,
author = {Tavakoli, Mostafa and Rahbarnia, Freydoon and Madjid Mirzavaziri, and A. R. Ashrafi},
title = {Further Results On the Third Zagreb Index of Graphs},
booktitle = {5th Conference on Algebraic Combinatorics and Graph Theory},
year = {2012},
location = {کاشان, IRAN},
keywords = {Tricyclic graph; Tetracyclic graph; Third Zagreb index.},
}
%0 Conference Proceedings
%T Further Results On the Third Zagreb Index of Graphs
%A Tavakoli, Mostafa
%A Rahbarnia, Freydoon
%A Madjid Mirzavaziri,
%A A. R. Ashrafi
%J 5th Conference on Algebraic Combinatorics and Graph Theory
%D 2012
