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Sharp upper bounds for Zagreb indices of bipartite graphs with a given diameter

✍ Scribed by Shuchao Li; Minjie Zhang

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
255 KB
Volume
24
Category
Article
ISSN
0893-9659

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✦ Synopsis

For a (molecular) graph, the first Zagreb index M 1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M 2 is equal to the sum of products of the degrees of a pair of adjacent vertices. In this work, we study the Zagreb indices of bipartite graphs of order n with diameter d and sharp upper bounds are obtained for M 1 (G) and M 2 (G) with G ∈ B(n, d), where B(n, d) is the set of all the n-vertex bipartite graphs with diameter d.

Furthermore, we study the relationship between the maximal Zagreb indices of graphs in B(n, d) and the diameter d. As a consequence, bipartite graphs with the largest, secondlargest and smallest Zagreb indices are characterized.

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