Sharp bounds of the Zagreb indices of k-trees

Authors:
John Estes;Bing Wei
Affiliations:
Department of Mathematics, University of Mississippi, University, USA 38677;Department of Mathematics, University of Mississippi, University, USA 38677
Venue:
Journal of Combinatorial Optimization
Year:
2014

Citing 3
Cited 0

An upper bound on the sum of squares of degrees in a graph

Discrete Mathematics
Independence polynomials of k-tree related graphs

Discrete Applied Mathematics
Sharp bounds for Zagreb indices of maximal outerplanar graphs

Journal of Combinatorial Optimization

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Abstract

For a graph G, the first Zagreb index M1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M2 is equal to the sum of the products of degrees of pairs of adjacent vertices. The Zagreb indices have been the focus of considerable research in computational chemistry dating back to Gutman and Trinajstić in 1972. In 2004, Das and Gutman determined sharp upper and lower bounds for M1 and M2 values for trees along with the unique trees that obtain the minimum and maximum M1 and M2 values respectively. In this paper, we generalize the results of Das and Gutman to the generalized tree, the k-tree, where the results of Das and Gutman are for k=1. Also by showing that maximal outerplanar graphs are 2-trees, we also extend a result of Hou, Li, Song, and Wei who determined sharp upper and lower bounds for M1 and M2 values for maximal outerplanar graphs.