Article
Full entry | Fulltext not available
(moving wall
24 months)
Feedback
Keywords:
graph irregularity; degree variance; Mostar index; graph energy; Laplacian eigenvalues
graph irregularity; degree variance; Mostar index; graph energy; Laplacian eigenvalues
Summary:
We give new bounds for several vertex-based and edge-based topological indices of graphs including the Albertson irregularity index, the degree variance index, and the Mostar index. In addition, we give a new upper bound for the energy of graph using the IRB index. Most of our results rely on a well-known characterization of the Laplacian spectral radius.
References:
[1] Abdo, H., Cohen, N., Dimitrov, D.: Graphs with maximal irregularity. Filomat 28 (2014), 1315-1322. DOI 10.2298/FIL1407315A | MR 3360039 | Zbl 1464.05048
[2] Abdo, H., Dimitrov, D.: The irregularity of graphs under graph operations. Discuss. Math., Graph Theory 34 (2014), 263-278. DOI 10.7151/dmgt.1733 | MR 3194036 | Zbl 1290.05062
[3] Albertson, M. O.: The irregularity of a graph. Ars Comb. 46 (1997), 219-225. MR 1470801 | Zbl 0933.05073
[4] Arizmendi, O., Hidalgo, J. Fernandez, Juarez-Romero, O.: Energy of a vertex. Linear Algebra Appl. 557 (2018), 464-495. DOI 10.1016/j.laa.2018.08.014 | MR 3848283 | Zbl 1396.05065
[5] Babić, D., Gutman, I.: More lower bounds for the total $\pi$-electron energy of alternant hydrocarbons. MATCH Commun. Math. Comput. Chem. 32 (1995), 7-17.
[6] Bollobás, B.: Extremal Graph Theory. London Mathematical Society Monographs 11. Academic Press, London (1978). MR 0506522 | Zbl 0419.05031
[7] Chen, X., Hou, Y., Lin, F.: Some new spectral bounds for graph irregularity. Appl. Math. Comput. 320 (2018), 331-340. DOI 10.1016/j.amc.2017.09.038 | MR 3722748 | Zbl 1426.05088
[8] Došlić, T., Martinjak, I., Škrekovski, R., Spužević, S. Tipurić, Zubac, I.: Mostar index. J. Math. Chem. 56 (2018), 2995-3013. DOI 10.1007/s10910-018-0928-z | MR 3860950 | Zbl 1406.92750
[9] Fiedler, M.: A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory. Czech. Math. J. 25 (1975), 619-633. DOI 10.21136/CMJ.1975.101357 | MR 0387321 | Zbl 0437.15004
[10] Gao, F., Xu, K., Došlić, T.: On the difference of Mostar index and irregularity of graphs. Bull. Malays. Math. Sci. Soc. (2) 44 (2021), 905-926. DOI 10.1007/s40840-020-00991-y | MR 4217094 | Zbl 1462.05080
[11] Goldberg, F.: A spectral bound for graph irregularity. Czech. Math. J. 65 (2015), 375-379. DOI 10.1007/s10587-015-0182-5 | MR 3360433 | Zbl 1349.05181
[12] Gutman, I.: The energy of a graph. Ber. Math.-Stat. Sekt. Forschungszent. Graz 103 (1978), 1-22. MR 0525890 | Zbl 0402.05040
[13] Gutman, I.: A formula for the Wiener number of trees and its extension to graphs containing cycles. Graph Theory Notes N. Y. 27 (1994), 9-15.
[14] I. Gutman, B. Ruščić, N. Trinajstić, C. F. Wilcox, Jr.: Graph theory and molecular orbitals. XII. Acyclic polyenes. J. Chem. Phys. 62 (1975), 3399-3405. DOI 10.1063/1.430994
[15] Gutman, I., Teodorović, A. V., Nedeljković, L.: Topological properties of benzenoid systems. Bounds and approximate formula for total $\pi$-electron energy. Theoretica Chim. Acta 65 (1984), 23-31. DOI 10.1007/BF02427577
[16] Gutman, I., Trinajstić, N.: Graph theory and molecular orbitals: Total $\phi$-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17 (1972), 535-538. DOI 10.1016/0009-2614(72)85099-1
[17] Jahanbani, A.: Some new lower bounds for energy of graphs. Appl. Math. Comput. 296 (2017), 233-238. DOI 10.1016/j.amc.2016.10.019 | MR 3572791 | Zbl 1411.05165
[18] Koolen, J. H., Moulton, V.: Maximal energy graphs. Adv. Appl. Math. 26 (2001), 47-52. DOI 10.1006/aama.2000.0705 | MR 1806691 | Zbl 0976.05040
[19] Li, X., Shi, Y., Gutman, I.: Graph Energy. Springer, New York (2012). DOI 10.1007/978-1-4614-4220-2 | MR 2953171 | Zbl 1262.05100
[20] McClelland, B. J.: Properties of the latent roots of a matrix: The estimation of $\pi$-electron energies. J. Chem. Phys. 54 (1971), 640-643. DOI 10.1063/1.1674889
[21] Merris, R.: Laplacian matrices of graphs: A survey. Linear Algebra Appl. 197-198 (1994), 143-176. DOI 10.1016/0024-3795(94)90486-3 | MR 1275613 | Zbl 0802.05053
[22] Miklavič, Š., Pardey, J., Rautenbach, D., Werner, F.: Maximizing the Mostar index for bipartite graphs and split graphs. Discrete Optim. 48 (2023), Article ID 100768, 7 pages. DOI 10.1016/j.disopt.2023.100768 | MR 4553782 | Zbl 1517.05040
[23] Mohar, B.: Some applications of Laplace eigenvalues of graphs. Graph Symmetry: Algebraic Methods and Applications NATO ASI Series. Series C. Mathematical and Physical Sciences 497. Kluwer, Dordrecht (1997), 225-275. MR 1468791 | Zbl 0883.05096
[24] Sharafdini, R., Réti, T.: On the transmission-based graph topological indices. Kragujevac J. Math. 44 (2020), 41-63. DOI 10.46793/KgJMat2001.041S | MR 4088864 | Zbl 1488.05121
[25] Snijders, T. A. B.: The degree variance: An index of graph heterogeneity. Social Networks 3 (1981), 163-174. DOI 10.1016/0378-8733(81)90014-9 | MR 0639871
Search
Partner of
