Sums of Powers of the Degrees of Graphs with k Cut Edges

Li, Shuchao; Yan, Lixia

doi:10.1007/s00373-010-0996-8

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2012

2024

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Cited by 3 publications

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“…Mathematicians also exhibited considerable interest in the properties of the Randić connectivity index; see [6,7,23,24,38,42,43,54,56]. The Randić connectivity index has also evolved into several variants [20,36,37,55,58,59,67].…”

Section: Introductionmentioning

confidence: 99%

Sharp bounds on Zagreb indices of cacti with k pendant vertices

Yang

Zhao

2012

Filomat

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For a (molecular) graph, the first Zagreb index M 1 is equal to the sum of squares of its vertex degrees, and the second Zagreb index M 2 is equal to the sum of products of degrees of pairs of adjacent vertices. A connected graph G is a cactus if any two of its cycles have at most one common vertex. In this paper, we investigate the first and the second Zagreb indices of cacti with k pendant vertices. We determine sharp bounds for M 1-, M 2-values of n-vertex cacti with k pendant vertices. As a consequence, we determine the n-vertex cacti with maximal Zagreb indices and we also determine the cactus with a perfect matching having maximal Zagreb indices.

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