Sharp bounds on Zagreb indices of cacti with k pendant vertices

Abstract

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.

Degree-Based Topological Indices

“…We quote here only some most recent works of this kind, [59][60][61][62][63][64][65] in which references to earlier studies can be found. Numerous papers on Zagreb indices are appearing also in mathematical journals; see the recent articles [66][67][68][69][70] and the references cited therein.…”

A new graph over semi-direct products of groups

“…As it is well known in graph theory, topological indices are very popular characterization methods for simple graphs. Therefore one may adapt some special indices (for example, Zagreb indices ( [18,29,36])) or irregularity index ( [4]) to the our new graph defined in this paper. On the other hand, as another future project, since the main idea in the paper [13] was to defined a new graph over a special algebraic structure, namely finite monogenic monoids, and since our main goal in here is quite similar with that paper (just by replacing monoids with groups), one may also study some special graph products (for instance, lexicographic, tensor, cartesian etc.)…”

On the Hyper-Zagreb Index of Some Operations on Graphs

“…In this paper we obtain the explicit formulae for hyper-Zagreb index of a graph for four operations in F-sums. For the computational techniques we refer [8,11,12,13].…”