20 research outputs found

    Three IndicesCalculationof Certain Crown Molecular Graphs

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    As molecular graph invariant topological indices, harmonic index, zeroth-order general Randic index and Co-PI index have been studied in recent years for prediction of chemicalphenomena. In this paper, we determine the harmonic index, zeroth-order general Randic index andCo-PI indexof certain r-crown molecular graphs

    On K-trees and Special Classes of K-trees

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    The class of k-trees is defined recursively as follows: the smallest k-tree is the k-clique. If G is a graph obtained by attaching a vertex v to a k-clique in a k-tree, then G is also a k-tree. Trees, connected acyclic graphs, are k-trees for k = 1. We introduce a new parameter known as the shell of a k-tree, and from the shell special subclasses of k-trees, tree-like k-trees, are classified. Tree-like k-trees are generalizations of paths, maximal outerplanar graphs, and chordal planar graphs with toughness exceeding one. Let fs = fs( G) be the number of independent sets of cardinality s of G. Then the polynomial I(G; x) = [special characters omitted] fs(G)x s is called the independence polynomial. All rational roots of the independence polynomials of paths are found, and the exact paths whose independence polynomials have these roots are characterized. Additionally trees are characterized that have ?1/q as a root of their independence polynomials for 1 ? q ? 4. The well known vertex and edge reduction identities for independence polynomials are generalized, and the independence polynomials of k-trees are investigated. Additionally, sharp upper and lower bounds for fs of maximal outerplanar graphs, i.e. tree-like 2-trees, are shown along with characterizations of the unique maximal outerplanar graphs that obtain these bounds respectively. These results are extensions of the works of Wingard, Song et al., and Alameddine. Let M1 and M2 be the first and second Zagreb index respectively. Then the minimum and maximum M1 and M2 values for k-trees are determined, and the unique k-trees that obtain these minimum and maximum values respectively are characterized. Additionally, the Zagreb indices of tree-like k-trees are investigated

    Electron Energy Studying of Molecular Structures via Forgotten Topological Index Computation

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    Sharp bounds for the modified multiplicative zagreb indices of graphs with vertex connectivity at most k

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    © 2019, University of Nis. All rights reserved. Zagreb indices and their modified versions of a molecular graph originate from many practical problems such as two dimensional quantitative structure-activity (2D QSAR) and molecular chirality. Nowadays, they have become important invariants which can be used to characterize the properties of graphs from different aspects. Let Vkn (or Ekn respectively) be a set of graphs of n vertices with vertex connectivity (or edge connectivity respectively) at most k. In this paper, we explore some properties of the modified first and second multiplicative Zagreb indices of graphs in Vkn and Ekn. By using analytic and combinatorial tools, we obtain some sharp lower and upper bounds for these indices of graphs in Vkn and Ekn. In addition, the corresponding extremal graphs which attain the lower or upper bounds are characterized. Our results enrich outcomes on studying Zagreb indices and the methods developed in this paper may provide some new tools for investigating the values on modified multiplicative Zagreb indices of other classes of graphs

    Reduced second Zagreb index of bicyclic graphs with pendent vertices

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    Reduced second Zagreb index has been defined recently. In this paper we characterized extremal bicyclic graphs with pendent vertices with respect to this novel index

    Graphical and numerical representations of DNA sequences: statistical aspects of similarity

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