Rocky Mountain Journal of Mathematics

Corrigendum to the minimum matching energy of bicyclic graphs with given girth

Abstract

The matching energy of a graph was introduced by Gutman and Wagner in 2012 and defined as the sum of the absolute values of zeros of its matching polynomial. In LiH:2016, the main result, Theorem 3.4, is in error. In this paper, the correct result is given.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 6 (2018), 1983-1992.

Dates
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1543028449

Digital Object Identifier
doi:10.1216/RMJ-2018-48-6-1983

Mathematical Reviews number (MathSciNet)
MR3879313

Zentralblatt MATH identifier
06987236

Citation

Ma, Gang; Ji, Shengjin; Wang, Jianfeng. Corrigendum to the minimum matching energy of bicyclic graphs with given girth. Rocky Mountain J. Math. 48 (2018), no. 6, 1983--1992. doi:10.1216/RMJ-2018-48-6-1983. https://projecteuclid.org/euclid.rmjm/1543028449

References

• J.A. Bondy and U.S.R. Murty, Graph theory, Springer, Berlin, 2008.
• L. Chen and J. Liu, The bipartite unicyclic graphs with the first $\lfloor (n-3)/4 \rfloor$ largest matching energies, Appl. Math. Comp. 268 (2015), 644–656.
• L. Chen and Y. Shi, Maximal matching energy of tricyclic graphs, MATCH Comm. Math. Comp. Chem. 73 (2015), 105–120.
• X. Chen, X. Li and H. Lian, The matching energy of random graphs, Discr. Appl. Math. 193 (2015), 102–109.
• E.J. Farrell, An introduction to matching polynomials, J. Comb. Th. 27 (1979), 75–86.
• I. Gutman, Acyclic systems with extremal Hückel $\pi$-electron energy, Th. Chim. Acta 45 (1977), 79–87.
• ––––, The matching polynomial, MATCH Comm. Math. Comp. Chem. 6 (1979), 75–91.
• ––––, The energy of a graph: Old and new results, in Algebraic combinatorics and applications, A. Betten, et al., eds., Springer, Berlin, 2001.
• I. Gutman, X. Li and J. Zhang, Graph energy, in Analysis of complex networks, From biology to linguistics, M. Dehmer and F. Emmert-Streib, eds., Wiley-VCH, Weinheim, 2009.
• I. Gutman and S. Wagner, The matching energy of a graph, Discr. Appl. Math. 160 (2012), 2177–2187.
• G. Huang, M. Kuang and H. Deng, Extremal graph with respect to matching energy for a random polyphenyl chain, MATCH Comm. Math. Comp. Chem. 73 (2015), 121–131.
• S. Ji, X. Li and Y. Shi, Extremal matching energy of bicyclic graphs, MATCH Comm. Math. Comp. Chem. 70 (2013), 697–706.
• S. Ji and H. Ma, The extremal matching energy of graphs, Ars Comb. 115 (2014), 243–355.
• S. Ji, H. Ma and G. Ma, The matching energy of graphs with given edge connectivity, J. Inequal. Appl. 2015 (2015), 415.
• H. Li, Y. Zhou and L. Su, Graphs with extremal matching energies and prescribed parameters, MATCH Comm. Math. Comp. Chem. 72 (2014), 239–248.
• H. Li and L. Zou, The minimum matching energy of bicyclic graphs with given girth, Rocky Mountain J. Math. 46 (2016), 1275–1291.
• S. Li and W. Yan, The matching energy of graphs with given parameters, Discr. Appl. Math. 162 (2014), 415–420.
• X. Li, Y. Shi and I. Gutman, Graph energy, Springer, New York, 2012.
• G. Ma, S. Ji, Q. Bian and X. Li, The maximum matching energy of bicyclic graphs with even girth, Discr. Appl. Math. 206 (2016), 203–210.
• ––––, The minimum matching energy of tricyclic graphs and given girth and without $K_4$-subdivision, ARS Comb. 132 (2017), 403–419.
• W. So and W. Wang, Finding the least element of the ordering of graphs with respect to their matching numbers, MATCH Comm. Math. Comp. Chem. 73 (2015), 225–238.
• W.H. Wang and W. So, On minimum matching energy of graphs, MATCH Comm. Math. Comp. Chem. 74 (2015), 399–410.
• K. Xu, K. Das and Z. Zheng, The minimal matching energy of $(n,m)$-graphs with a given matching number, MATCH Comm. Math. Comp. Chem. 73 (2015), 93–104.