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Pure Mathematics 2025
关于自环图能量的新下界
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Abstract:
设
为
个顶点的自环图,其通过在简单图
上向点集
中的点添加自环得到。自环图
的能量由Gutman等学者定义为
,其中
为
的邻接特征值,
为
中自环的个数。本文利用矩阵理论给出了一个自环图最大特征值上界的充要条件,并利用这个上界和Ozeki不等式分别给出了自环图能量
的新下界。
Let
be a self-loop graph with
vertices obtained from a simple graph
by attaching one self-loop at each vertex in
[1] | Gutman, I. (1978) The Energy of a Graph. Graz Forschungszentrum Mathematisch-Statistische Sektion Berichte, 103, 1-22. |
[2] | Gutman, I., Vidovic, D., Cmiljanovic, N., Milosavljevic, S. and Radenkovic, S. (2003) Graph Energy—A Useful Molecular Structure-Descriptor. Indian Journal of Chemistry A, 42, 1309-1311. |
[3] | Dehmer, M., Li, X. and Shi, Y. (2014) Connections between Generalized Graph Entropies and Graph Energy. Complexity, 21, 35-41. https://doi.org/10.1002/cplx.21539 |
[4] | Arizmendi, G. and Arizmendi, O. (2023) The Graph Energy Game. Discrete Applied Mathematics, 330, 128-140. https://doi.org/10.1016/j.dam.2023.01.030 |
[5] | Li, X.L. Shi, Y.T. and Gutman, I. (2012) Graph Energy. Springer. https://doi.org/10.1007/978-1-4614-4220-2 |
[6] | McClelland, B.J. (1971) Properties of the Latent Roots of a Matrix: The Estimation of π-Electron Energies. The Journal of Chemical Physics, 54, 640-643. https://doi.org/10.1063/1.1674889 |
[7] | Caporossi, G., Cvetković, D., Gutman, I. and Hansen, P. (1999) Variable Neighborhood Search for Extremal Graphs. 2. Finding Graphs with Extremal Energy. Journal of Chemical Information and Computer Sciences, 39, 984-996. https://doi.org/10.1021/ci9801419 |
[8] | Koolen, J.H. and Moulton, V. (2001) Maximal Energy Graphs. Advances in Applied Mathematics, 26, 47-52. https://doi.org/10.1006/aama.2000.0705 |
[9] | Agudelo, N. and Rada, J. (2016) Lower Bounds of Nikiforov’s Energy over Digraphs. Linear Algebra and its Applications, 494, 156-164. https://doi.org/10.1016/j.laa.2016.01.008 |
[10] | Gutman, I., Redžepović, I., Furtula, B. and Sahal, A.M. (2021) Energy of Graphs with Self-Loops. MATCH Communications in Mathematical and in Computer Chemistry, 87, 645-652. https://doi.org/10.46793/match.87-3.645g |
[11] | Gutman, I. (1979) Topological Studies on Heteroconjugated Molecules: Alternant Systems with One Heteroatom. Theoretica Chimica Acta, 50, 287-297. https://doi.org/10.1007/bf00551336 |
[12] | Gutman, I. (1990) Topological Studies on Heteroconjugated Molecules. VI. Alternant Systems with Two Heteroatoms. Zeitschrift für Naturforschung A, 45, 1085-1089. https://doi.org/10.1515/zna-1990-9-1005 |
[13] | Liu, J., Chen, Y., Dimitrov, D. and Chen, J. (2023) New Bounds on the Energy of Graphs with Self-Loops. MATCH—Communications in Mathematical and in Computer Chemistry, 91, 779-796. https://doi.org/10.46793/match.91-3.779l |
[14] | Shetty, S.S. and Bhat K, A. (2023) On the First Zagreb Index of Graphs with Self-Loops. AKCE International Journal of Graphs and Combinatorics, 20, 326-331. https://doi.org/10.1080/09728600.2023.2246515 |
[15] | Izumino, S., Mori, H. and Seo, Y. (1998) On Ozeki’s Inequality. Journal of Inequalities and Applications, 1998, Article ID: 329791. https://doi.org/10.1155/s1025583498000149 |