THE Minimum Pendant Dominating Randic Graph Energy
Resumen
In this research paper, we introduce the concept of Minimum Pendant Dominating Randic Graph Energy, denoted by , and compute its value for several well-known graph families, including the complete graph, complete bi- partite graph, bi-star graph, cocktail party, and barbell graph. Additionally, we investigate theoretical upper and lower bounds for , offering insights into the behavior and range of this energy measure across various classes of graphs.
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[1] C. Adiga, A. Bayad, I. Gutman and S. A. Srinivas (2012) – “The minimum covering energy of a graph” - Kragujevac Journal of Science, volume 34, pages 39 - 56.
[2] S. Alikhani and N. Ghanbari (2015), “Randić energy of specific graphs”, Applied Mathematics and Computation, volume 269, pages 722 - 730. DOI: 10.1016/j.amc.2015.07.112
[3] R. Balakrishnan (2004), “The energy of a graph”, Linear Algebra and its Applications, volume 387, pages 287 – 295. https://doi.org/10.1016/j.laa.2004.02.038
[4] Ş. B. Bozkurt, A. D. Güngör, I. Gutman and A. S. Çevik (2010), “Randić Matrix and Randić Energy”, MATCH Communications in Mathematical and in Computer Chemistry, volume 64, pages 239 - 250 [On line]. Available: https://bit.ly/3iChvsG
[5] Ş. B. Bozkurt, A. D. Güngör, and I. Gutman (2010), “Randić Spectral Radius and Randić Energy”, MATCH Communications in Mathematical and in Computer Chemistry, volume 64, pages 321 - 334.
[6] Z. Chu, S. Nazeer, T. J. Zia, I. Ahmed and S. Shahid (2019), “Some New Results on Various Graph Energies of the Splitting Graph”, Journal of Chemistry, volume 2019, Article ID 7214047, pages 12. DOI: 10.1155/2019/7214047
[7] D. Cvetković, P. Rowlinson and S. Simić (2010), “An Introduction to The Theory of Graph Spectra”, (London Mathematical Society Student Texts, No. 75). Cambridge, UK: Cambridge University Press.
[8] S. C. Gong, X. Li, G. H. Xu, I. Gutman and B. Furtula (2017), “Border energetic Graphs”, MATCH Communications in Mathematical and in Computer Chemistry, volume 77, pages 589 – 594.
[9] I. Gutman (1978), "The Energy of a Graph", Berichte der Mathematisch-Statistischen Sektion im Forschungszentrum Graz, volume 103, pages 1 – 22.
[10] I. Gutman and B. Furtula (2008), “Recent results in the theory of Randić index”, (Mathematical Chemistry Monographs No. 6), Kragujevac, Serbia: University of Kragujevac.
[11] I. Gutman, B. Furtula and S. B. Bozkurt (2014), “On Randic Energy”, Linear Algebra and its Applications, volume 442, pages 50 – 57. DOI: 10.1016/j.laa.2013.06.010
[12] X. Li and I. Gutman, (2006), “Mathematical aspects of Randić type molecular structure descriptors”, (Mathematical Chemistry Monographs No. 1). Kragujevac, Serbia: University of Kragujevac.
[13] X. Li, Y. Shi and I. Gutman (2010), “Graph Energy”, New York, NY: Springer. https://doi.org/10.1007/978-1-4614-4220-2
[14] M. Randić (1975), “Characterization of molecular branching”, Journal of the American Chemical Society, volume 97(23), pages 6609 – 6615. https://doi.org/10.1021/ja00856a001
[15] M. Randić (2008), “On history of the Randić index and emerging hostility towards chemical graph theory”, MATCH Communications in Mathematical and in Computer Chemistry, volume 59(1), pages 5 – 124. Retrieved from https://bit.ly/3ZyjnDm
[16] O. Rojo and L. Medina, (2012), “Construction of bipartite graphs having the same Randić energy”, MATCH Communications in Mathematical and in Computer Chemistry, volume 68(3), pages 805 – 814. Retrieved from https://bit.ly/3J7HHEb
[17] P. Siva Kota Reddy, K. N. Prakash and V. M. Siddalingaswamy (2017), “Minimum dominating Randić energy of a graph”, Vladikavkaz Mathematical Journal, volume 19(2), Article ID 6506. https://doi.org/10.23671/VNC.2017.2.6506
[18] S. K. Vaidya and G. K. Rathod (2021), “Randić energy of various graphs”, Advances and Applications in Discrete Mathematics, volume 28(2), pages 267 – 286. https://doi.org/10.17654/dm028020267
[19] H. B. Walikar, H. S. Ramane and P. R. Hampiholi, (1999), “On the energy of a graph”, In R. Balakrishnan, H. M. Mulder, and A. Vijaykumar (Eds.), Graph Connections, pages 120–123 New Delhi, India: Allied Publishers
[2] S. Alikhani and N. Ghanbari (2015), “Randić energy of specific graphs”, Applied Mathematics and Computation, volume 269, pages 722 - 730. DOI: 10.1016/j.amc.2015.07.112
[3] R. Balakrishnan (2004), “The energy of a graph”, Linear Algebra and its Applications, volume 387, pages 287 – 295. https://doi.org/10.1016/j.laa.2004.02.038
[4] Ş. B. Bozkurt, A. D. Güngör, I. Gutman and A. S. Çevik (2010), “Randić Matrix and Randić Energy”, MATCH Communications in Mathematical and in Computer Chemistry, volume 64, pages 239 - 250 [On line]. Available: https://bit.ly/3iChvsG
[5] Ş. B. Bozkurt, A. D. Güngör, and I. Gutman (2010), “Randić Spectral Radius and Randić Energy”, MATCH Communications in Mathematical and in Computer Chemistry, volume 64, pages 321 - 334.
[6] Z. Chu, S. Nazeer, T. J. Zia, I. Ahmed and S. Shahid (2019), “Some New Results on Various Graph Energies of the Splitting Graph”, Journal of Chemistry, volume 2019, Article ID 7214047, pages 12. DOI: 10.1155/2019/7214047
[7] D. Cvetković, P. Rowlinson and S. Simić (2010), “An Introduction to The Theory of Graph Spectra”, (London Mathematical Society Student Texts, No. 75). Cambridge, UK: Cambridge University Press.
[8] S. C. Gong, X. Li, G. H. Xu, I. Gutman and B. Furtula (2017), “Border energetic Graphs”, MATCH Communications in Mathematical and in Computer Chemistry, volume 77, pages 589 – 594.
[9] I. Gutman (1978), "The Energy of a Graph", Berichte der Mathematisch-Statistischen Sektion im Forschungszentrum Graz, volume 103, pages 1 – 22.
[10] I. Gutman and B. Furtula (2008), “Recent results in the theory of Randić index”, (Mathematical Chemistry Monographs No. 6), Kragujevac, Serbia: University of Kragujevac.
[11] I. Gutman, B. Furtula and S. B. Bozkurt (2014), “On Randic Energy”, Linear Algebra and its Applications, volume 442, pages 50 – 57. DOI: 10.1016/j.laa.2013.06.010
[12] X. Li and I. Gutman, (2006), “Mathematical aspects of Randić type molecular structure descriptors”, (Mathematical Chemistry Monographs No. 1). Kragujevac, Serbia: University of Kragujevac.
[13] X. Li, Y. Shi and I. Gutman (2010), “Graph Energy”, New York, NY: Springer. https://doi.org/10.1007/978-1-4614-4220-2
[14] M. Randić (1975), “Characterization of molecular branching”, Journal of the American Chemical Society, volume 97(23), pages 6609 – 6615. https://doi.org/10.1021/ja00856a001
[15] M. Randić (2008), “On history of the Randić index and emerging hostility towards chemical graph theory”, MATCH Communications in Mathematical and in Computer Chemistry, volume 59(1), pages 5 – 124. Retrieved from https://bit.ly/3ZyjnDm
[16] O. Rojo and L. Medina, (2012), “Construction of bipartite graphs having the same Randić energy”, MATCH Communications in Mathematical and in Computer Chemistry, volume 68(3), pages 805 – 814. Retrieved from https://bit.ly/3J7HHEb
[17] P. Siva Kota Reddy, K. N. Prakash and V. M. Siddalingaswamy (2017), “Minimum dominating Randić energy of a graph”, Vladikavkaz Mathematical Journal, volume 19(2), Article ID 6506. https://doi.org/10.23671/VNC.2017.2.6506
[18] S. K. Vaidya and G. K. Rathod (2021), “Randić energy of various graphs”, Advances and Applications in Discrete Mathematics, volume 28(2), pages 267 – 286. https://doi.org/10.17654/dm028020267
[19] H. B. Walikar, H. S. Ramane and P. R. Hampiholi, (1999), “On the energy of a graph”, In R. Balakrishnan, H. M. Mulder, and A. Vijaykumar (Eds.), Graph Connections, pages 120–123 New Delhi, India: Allied Publishers
Publicado
2025-10-30
Número
Sección
Research Articles
Derechos de autor 2025 Boletim da Sociedade Paranaense de Matemática
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