JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (2): 34-40.doi: 10.6040/j.issn.1671-9352.0.2023.067

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Bounds of weighted Szeged index of two kinds of tree graphs

HU Jiao, LIU Mengmeng   

  1. School of Mathematics and Science, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2025-02-14

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Abstract: Given a graph G, the weighted Szeged index of a graph G, denoted by Sw(G)=∑uv=e∈E(G)(dG(u)+dG(v))nGu(e)nGv(e), where dG(u)is the degree of u in G. For edge uv=e∈E(G), nu(e)represents the number of vertices closer to vertex u than vertex v in graph G. Some graph transformations are given, by using these graph transformations, the upper bound and lower bound of weighted Szeged index of blossomed stars and the upper bound of weighted Szeged index of trees with given diameters are obtained, and the corresponding extreme value graphs are characterized.

Key words: weighted Szeged index, blossomed star, tree

CLC Number: 

  • O157.5
[1] BONDY J A, MURTY U S R. Graph theory[M]. Berlin: Springer, 2008.
[2] WIENER H. Structural determination of paraffin boiling points[J]. Journal of the American Chemical Society, 1947, 69(1):17-20.
[3] GUTMAN I. A formula for the Wiener number of trees and its extension to graphs containing cycles[J]. Graph Theory Notes, 1994, 27(9):9-15.
[4] SIMIC S, GUTMAN I, BALTIC V. Some graphs with extremal Szeged index[J]. Mathematica Slovaca, 2000, 50(1):1-15.
[5] LIU Yan, YU Aimei, LU Mei, et al. On the Szeged index of unicyclic graphs with given diameter[J]. Discrete Applied Mathematics, 2017, 233:118-130.
[6] ZHOU Bo, CAI Xiaochun, DU Zhibin. On Szeged indices of unicyclic graphs[J]. Match Communications in Mathematical and in Computer Chemistry, 2010, 63:113-132.
[7] ILIC A, MILOSAVLJEVIC N. The weighted vertex PI index[J]. Mathematical and Computer Modelling, 2013, 57(3/4):623-631.
[8] NAGARAJAN S, PATTABIRAMAN K, CHANDRASEKHARAN M. Weighted Szeged index of generalized hierarchical product of graphs[J]. General Mathematics Notes, 2014, 23(2):85-95.
[9] PATTABIRAMAN K, KANDAN P. Weighted Szeged indices of some graph operations[J]. Transactions on Combinatorics, 2016, 5(1):25-35.
[10] ATANASOV R, FURTULA B, SKREKOVSKI R. Trees with minimum weighted Szeged index are of a large diameter[J]. Symmetry, 2020, 12(5):793.
[11] BOK J, FURTULA B. On extremal graphs of weighted Szeged index[J]. Match Communications in Mathematical and in Computer Chemistry, 2019, 82:93-109.
[12] DOLATI A, MOTEVALIAN I, EHYAEE A. Szeged index, edge Szeged index, and semi-star trees[J]. Discrete Applied Mathematics, 2010, 158(8):876-881.
[13] CHEN Wuxian, YAN Weigen. On the energy of blossomed stars[J]. Match Communications in Mathematical and in Computer Chemistry, 2020, 83:623-630.
[14] HUA Hongbo. Trees with given diameter and minimum second Geometric-Arithmetic index[J]. Match Communications in Mathematical and in Computer Chemistry, 2010, 64:631-638.
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