On Laplacian resolvent energy of graphs

Bhatnagar, Sandeep; Merajuddin, Siddiqui; Pirzada, Shariefuddin

doi:10.22108/toc.2022.133236.1983

تعداد نشریات	43
تعداد شماره‌ها	1,486
تعداد مقالات	12,203
تعداد مشاهده مقاله	23,238,390
تعداد دریافت فایل اصل مقاله	10,021,169

	On Laplacian resolvent energy of graphs
Transactions on Combinatorics
دوره 12، شماره 4، اسفند 2023، صفحه 217-225 اصل مقاله (445.32 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2022.133236.1983
نویسندگان
Sandeep Bhatnagar¹؛ Siddiqui Merajuddin¹؛ Shariefuddin Pirzada^* ²
¹Department of Applied Mathematics, Aligarh Muslim University, Aligarh, India
²Department of Mathematics, University of Kashmir, Srinagar, India
چکیده
Let $G$ be a simple connected graph of order $n$ and size $m$. The matrix $L(G)=D(G)-A(G)$ is the Laplacian matrix of $G$, where $D(G)$ and $A(G)$ are the degree diagonal matrix and the adjacency matrix, respectively. For the graph $G$, let $d_{1}\geq d_{2}\geq \cdots d_{n}$ be the vertex degree sequence and $\mu_{1}\geq \mu_{2}\geq \cdots \geq \mu_{n-1}>\mu_{n}=0$ be the Laplacian eigenvalues. The Laplacian resolvent energy $RL(G)$ of a graph $G$ is defined as $RL(G)=\sum\limits_{i=1}^{n}\frac{1}{n+1-\mu_{i}}$. In this paper, we obtain an upper bound for the Laplacian resolvent energy $RL(G)$ in terms of the order, size and the algebraic connectivity of the graph. Further, we establish relations between the Laplacian resolvent energy $RL(G)$ with each of the Laplacian-energy-Like invariant $LEL$, the Kirchhoff index $Kf$ and the Laplacian energy $LE$ of the graph.
کلیدواژه‌ها
Laplacian resolvent energy؛ Laplacian energy؛ Laplacian-energy-like invariant؛ Kirchhoff index

مراجع
[1] L. E. Allem, J. Capaverde, V. Trevisan, I. Gutman, E. Zogic and E. Glogic, Resolvent energy of unicyclic, bicyclic and tricyclic graphs, MATCH Commun. Math. Comput. Chem., 77 (2017) 95–104. [2] A. Cafure, D. A. Jaume, L. N. Grippo, A. Pastine, M. D. Safe, V. Trevisan and I. Gutman, Some results for the (signless) Laplacian resolvent, MATCH Commun. Math.Comput. Chem., 77 (2017) 105–114. [3] Z. Du, Asymptotic expressions for resolvent energies of paths and cycles, MATCH Commun. Math. Comput. Chem., 77 (2017) 85–94. [4] A. Farrugia, The increase in the resolvent energy of a graph due to the addition of a new edge, Appl. Math. Comput., 321 (2018) 25–36. [5] B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem., 53 (2015) 1184–1190. [16] P. Milosevic, E. Milovanovic, M. Matejic and I. Milovanovic, On relations between Kirchhoff index, Laplacian energy, Laplacian-energy-like invariant and degree deviation of graphs, Filomat, 34 (2020) 1025–1033. [17] I. Milovanovic, M. Matejic, E. Glogic and E. Milovanovic, Some new lower bounds for the Kirchhoff index of a graph, Bull. Aust. Math. Soc., 97 (2018) 1–10. [18] S. Pirzada and H. A. Ganie, On Laplacian-energy-like invariant and Incidence energy, Trans. Comb., 4 (2015) 25–35. [19] S. Pirzada, H. A.Ganie and I. Gutman, On on Laplacian-energy-like invariant and Kirchhoff index, MATCH Com- mun. Math. Comput. Chem., 73 (2015) 41–60. [20] S. Pirzada, H. A. Ganie and I. Gutman, Comparison between Laplacian-energy-like invariant and the Kirchhoff index, El. J. Linear Algebra, 31 (2016) 27–41. [21] S. Pirzada, An Introduction to Graph Theory, Universities Press, Orient BlackSwan Hyderabad, 2012. [22] J. Radon, Theorie und Anwendungen der absolut Additiven Mengenfunktionnem, Sitzungsber Acad. Wissen, Wien, 122 (1913) 1295–1438. [23] B. C. Rennie, On a class of inequalities, J. Australian Math. Soc., 3 (1963) 442–448. [24] H. Wiener, Structural determination of paraffin boilling points, J. Amer. Chem. Soc., 69 (1947) 17–20. [25] Z. Zhu, Some extremal properties of the resolvent energy, Estrada and resolvent Estrada indices of graphs, J. Math. Anal. Appl., 447 (2017) 957–970. [6] I. Gutman and B. Zhou, Laplacian energy of a graph, Linear Algebra Appl., 414 (2006) 29–37. [7] I. Gutman and B. Mohar, The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci., 36 (1996) 982–985. [8] I. Gutman, B. Furtula, E. Zogic and E. Glogic, Resolvent energy of graphs, MATCH Commun. Math. Comput. Chem., 75 (2016) 279–290. [9] I. Gutman, B. Furtula, E. Zogic and E. Glogic, Resolvent energy of graphs, MATCH Commun. Math. Comput. Chem., 75 (2016) 279–290. [10] D. J. Klein and M. Randic, Resistence distance, J. Math. Chem., 12 (1993) 81–95. [11] J. Liu and B. A. Liu, Laplacian-energy-like invariant, MATCH Commun. Math. Comput. Chem., 59 (2008) 355–372. [12] B. Liu and Z. Y. Liu, A survey on the Laplacian-energy-like invariant, MATCH Commun. Math. Comput. Chem., 66 (2011) 713–730. [13] M. Matejic, E. Zogic, E. Milovanovic and I. Milovanovic, A note on the Laplacian resolvent energy of graphs, Asian European J. Math., 13 (2020) 6 p. [14] I. Milovanovic, E. Milovanovic, E. Glogic and M. Matejic, On Kirchhoff index, Laplacian energy and their relation, MATCH Commun. Math. Comput. Chem., 81 (2019) 405–418. [15] E. I. Milovanovic, I. Z. Milovanovic and M. M. Matejic, On relation between Kirchhoff index and Laplacian-energy- like invariant of graphs, Math. Int. Res., 2 (2017) 141–154.
آمار تعداد مشاهده مقاله: 603 تعداد دریافت فایل اصل مقاله: 591

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

اخبار و اعلانات

آمار

On Laplacian resolvent energy of graphs