JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (8): 68-77.doi: 10.6040/j.issn.1671-9352.0.2023.422

Previous Articles    

Lower bound of Mostar index with respect to tricyclic graphs

WANG Hui, LIU Mengmeng*   

  1. School of Mathematics and Science, Lanzhou Jiaotong University, Lanzhou 730070, China
  • Published:2025-07-25

PDF (PC)

13

Abstract: The Mostar index M(G) of a connected graph G is defined as M(G)=∑e=uv∈E(G)|nu(e)-nv(e)|, where nu(e) and nv(e) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u. The lower bound of the Mostar index among all tricyclic graphs is established, and the extremal graphs that attained the lower bound are determined.

Key words: Mostar index, tricyclic graph, extremal graph

CLC Number: 

  • O157.5
[1] BONDY J A, MURTY U S R. Graph theory[M]. London: Springer, 2008.
[2] DOŠLI C T, MARTINJAK I, ŠKREKOVSKI R, et al. Mostar index[J]. Journal of mathematical chemistry, 2018, 56: 2995-3013.
[3] DEHGARDI N, AZARI M. More on Mostar index[J]. Appl Math E-Notes, 2020, 20:316-322.
[4] HAYAT F, ZHOU Bo. On cacti with large Mostar index[J]. Filomat, 2019, 33(15):4865-4873.
[5] TEPEH A. Extremal bicyclic graphs with respect to Mostar index[J]. Applied Mathematics and Computation, 2019, 355:319-324.
[6] TRATNIK N. Computing the Mostar index in networks with applications to molecular graphs[J]. Iranian Journal of Mathematical Chemistry, 2021, 12(1):1-18.
[7] GHANBARI N, ALIKHANI S. Mostar index and edge Mostar index of polymers[J]. Computational and Applied Mathematics, 2021, 40:1-21.
[8] HAVARE O C. Mostar index(Mo)and edge Mo index for some cycle related graphs[J]. Rom J Math Comput Sci, 2020, 10:53-66.
[9] GHALAVAND A, ASHRAFI A R, HAKIMI-NEZHAAD M. On Mostar and edge Mostar indices of graphs[J]. Journal of Mathematics, 2021, 2021(1):6651220.
[10] AROCKIARAJ M, CLEMENT J, TRATNIK N. Mostar indices of carbon nanostructures and circumscribed donut benzenoid systems[J]. International Journal of Quantum Chemistry, 2019, 119(24):1-11.
[11] ALI A, DOŠLI C T. Mostar index: results and perspectives[J]. Applied mathematics and computation, 2021, 404:1-9.
[12] LI S C, LI X C, ZHU Z X. On tricyclic graphs with minimal energ[J]. MATCH Commun Math Comput Chem, 2008, 59(2):397-419.
[13] CHEN L L, LI X L, LIU M M. Tricyclic graphs with maximal revised Szeged index[J]. Discrete Applied Mathematics, 2014, 177:71-79.
[1] WU Yi-fan, WANG Guang-fu. Extremal graphs on distance spectral radius of polyomino chains [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(2): 84-91.
[2] LAI Jin-hua, LIU Meng-meng. On minimum Steiner k-Wiener index of trees with perfect matching [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 66-71.
[3] YANG Chen, MA Hai-cheng. Positive and negative inertia indexes and nullity of two special kinds of tricyclic graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 32-37.
[4] ZOU Jin-yu, REN Hai-zhen. The total number of matchings of L*n,p [J]. J4, 2013, 48(2): 49-52.
[5] LUO Zhao-yang1,2, CHEN Xiang-lian1, SUN De-rong1. Six-member ring spiro chains with extremal Wiener and  hyper-Wiener indices [J]. J4, 2010, 45(12): 16-21.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd