The laplacian minimum pendant dominating degree energy of a graph
Résumé
In this research paper, we introduce the concept of laplacian minimum pendant dominating degree energy of a graph, denoted by LEPD (G), and compute its value for several well-known graph families, including the complete graph, complete bipartite graph, double star graph and dumbbell graph. In addition, we analyze the theoretical upper and lower bounds of LEPD (G), shedding light on its behavior and possible range over different categories of graphs.
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Références
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Journal of Scientific Engineering and Science, vol. 1, No. 7, pp. 13-15.
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ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM), pp. 2328-3629.
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International Journal of Pure and Applied Mathematics, vol. 89, No. 4, pp. 565-581.
23. B. Zhou (2009), New upper bounds for Laplacian energy, MATCH Communications in Mathematics and in Computer
Chemistry, vol. 62, pp. 553-560.
24. B. Zhou (2008), On the sum of powers of the Laplacian eigenvalues of graphs, Linear Algebra and Its Applications,
vol. 429, pp. 2239-2246. DOI: 10.1016/j.laa.2008.06.023
25. B. Zhou (2008), On the sum of powers of the Laplacian eigenvalues of graphs, Linear Algebra and Its Applications,
vol. 429(10), pp. 2239–2246. https://doi.org/10.1016/j.laa.2008.06.023
26. B. Zhou and I. Gutman (2007), On Laplacian energy of graphs, MATCH Communications in Mathematics and in
Computer Chemistry, vol. 57, pp. 211-220.
Journal of Science, vol 34, pp. 39–56.
2. T. AleksiˆAˇtc (2008), Upper Bounds for Laplacian Energy of Graphs. MATCH Communications in Mathematics and
Computer Chemistry, vol. 60, pp. 435-439.
3. R. B. Bapat and S. Pati (2004), Energy of a graph is never an odd integer, Bulletin of the Kerala Mathematical
Association, vol. 1, pp. 129–132.
4. R. B. Bapat (2011), Graphs and Matrices, Hindustan Book Agency, page no. 32.
5. K. C. Das, I. Gutman and B. Furtula (2017), On spectral radius and energy of extended adjacency matrix of graphs,
Applied Mathematics and Computation, vol. 296, pp. 116-123. DOI: 10.1016/j.amc.2016.10.029
6. N. N. M. de Abreu, C. T. M. Vinagre, A. S. Bonif´acio and I. Gutman (2008), The Laplacian energy of some Laplacian
integral graphs, MATCH Communications in Mathematics and in Computer Chemistry, vol. 60, pp. 447-460.
7. G. H. Fath-Tabar, A. R. Ashrafi and I. Gutman (2008), Note on Laplacian energy of graphs, Bulletin de l’Acad´emie
Serbe des Sciences et des Arts, Classe des Sciences Math´ematiques et Naturelles, vol. 137(33), pp. 1-10.
8. I. Gutman (1978), The Energy of a Graph, Berichte der Mathematisch-Statistischen Sektion im Forschungszentrum
Graz, vol. 103, pp. 1–22.
9. I. Gutman (2001) The energy of a graph: Old and new results, In A. Betten, A. Kohnert, R. Laue, and A. Wassermann
(Eds.), Algebraic Combinatorics and Applications, Springer, Berlin, pp. 196-211.
10. I. Gutman and B. Zhou (2006), Laplacian energy of a graph, Linear Algebra and its Applications, vol. 414(1), pp.
29–37. DOI: 10.1016/j.laa.2005.09.008
11. I. Gutman, N. N. M. de Abreu, C. T. M. Vinagre, A. S. Bonif´acio and S. Radenkovi´c (2008), Relation between energy
and Laplacian energy , MATCH Communications in Mathematics and in Computer Chemistry, vo;. 59, pp. 343-354.
12. J. Liu and B. Liu (2009), On relation between energy and Laplacian energy, MATCH Communications in Mathematics
and in Computer Chemistry, vol. 61, pp. 403-406.
13. B. J. McClelland (1971), Properties of the latent roots of a matrix-The estimation of pi-electron energies, Journal of
Chemical Physics, vol. 54, pp. 640–643.
14. I. ˇZ. Milovanovi´c, E. I. Milovanovi´c and A. Zaki´c (2014), A short note on graph energy, MATCH Communications in
Mathematics and in Computer Chemistry, vol. 72(1), pp. 179–182.
15. A. R. Nagalakshmi, A. S. Shrikanth, G. K. Kalavathi and K. S. Sreekeshava, “The Degree Energy of a Graph”, MDPI,
Σ Mathematics, volume 12 (2024) page 2699. https://doi.org/10.3390/math12172699
16. K. Nataraj, Puttaswamy and S. Purushothama (2024), The Laplacian Minimum Pendant Dominating Energy of a
Graph, Tuijin Jishu/Journal of Propulsion Technology, ISSN: 1001-4055, vol. 45, No. 3, pp. 3140-3150.
17. S. R. Nayaka, Puttaswamy and S. Purushothama (2020), Pendant Domination in Graphs, Journal of Combinatorial
Mathematics and Combinatorial Computing, Vol. 112, pp. 219-230
18. S. R. Nayaka, Puttaswamy and S. Purushothama (2017), Complementary Pendant Domination in Graphs, International
Journal of Pure and Applied Mathematics, Vol. 113, No. 11, pp. 179-187.
19. S. R. Nayaka, Puttaswamy and S. Purushothama (2017), Pendant Domination in Some Generalized Graphs, International
Journal of Scientific Engineering and Science, vol. 1, No. 7, pp. 13-15.
20. S. R. Nayaka, Puttaswamy and S. Purushothama (2019), Minimum Pendant Dominating energy of a Graph, AIJRSTEM,
ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM), pp. 2328-3629.
21. M. R. Rajesh Kanna, B. N. Dharmendra and G. Sridhara (2013), Minimum dominating energy of a graph, International
Journal of Pure and Applied Mathematics, vol. 85(4), pp. 707-718.
22. M. R. Rajesh Kanna, B. N. Dharmendra and G. Sridhara (2013), Laplacian Minimum Dominating Energy of a Graph,
International Journal of Pure and Applied Mathematics, vol. 89, No. 4, pp. 565-581.
23. B. Zhou (2009), New upper bounds for Laplacian energy, MATCH Communications in Mathematics and in Computer
Chemistry, vol. 62, pp. 553-560.
24. B. Zhou (2008), On the sum of powers of the Laplacian eigenvalues of graphs, Linear Algebra and Its Applications,
vol. 429, pp. 2239-2246. DOI: 10.1016/j.laa.2008.06.023
25. B. Zhou (2008), On the sum of powers of the Laplacian eigenvalues of graphs, Linear Algebra and Its Applications,
vol. 429(10), pp. 2239–2246. https://doi.org/10.1016/j.laa.2008.06.023
26. B. Zhou and I. Gutman (2007), On Laplacian energy of graphs, MATCH Communications in Mathematics and in
Computer Chemistry, vol. 57, pp. 211-220.
Publiée
2025-11-01
Rubrique
Advances in Nonlinear Analysis and Applications
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