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EIGENVALUES AND ENERGY OF ARITHMETIC FUNCTION GRAPH OF A FINITE GROUP

P. SIVA KOTA REDDY|R. Rajendra|R. Kemparaju
장전수학회 (Jangjeon Mathematical Society)|2024.01|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제27권 제1호|pp. 29-34|DOI 10.17777/pjms.2024.27.1.003

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참고문헌

키워드

GraphEigenvaluesEnergyGroupArith- metic function graph
주제분류수학

초록

Given an arithmetical function h, the arithmetic function graph Gh(G) of a nite group G with respect to h is de ned as a graph with vertex set V (Gh(G)) = G and any two distinct vertices a and b are adjacent in Gh(G) if and only if h(jajjbj) = h(jaj)h(jbj). The energy of a graph is the sum of the absolute values of the eigenvalues of the adjacency matrix of the graph. In this paper, we discuss some results on eigenvalues and energy of arithmetic function graphs of nite groups.

Abstract

Given an arithmetical function h, the arithmetic function graph Gh(G) of a nite group G with respect to h is de ned as a graph with vertex set V (Gh(G)) = G and any two distinct vertices a and b are adjacent in Gh(G) if and only if h(jajjbj) = h(jaj)h(jbj). The energy of a graph is the sum of the absolute values of the eigenvalues of the adjacency matrix of the graph. In this paper, we discuss some results on eigenvalues and energy of arithmetic function graphs of nite groups.

참고문헌 (25)

  1. R. B. Bapat, "Graphs and matrices, Universitext" (2010), Springer
  2. A. E. Brouwer, "Spectra of Graphs - Monograph" (2011), Springer
  3. D. M. Burton, "Elementary number theory" (2012), McGraw Hill Education(India)
  4. D. M. Cvetkovic, "Spectra of Graphs" (1979), Academic Press
  5. H. R. Dorbidi, "A note on the coprime graph of a group", Int. J. Group Theory, 5(4), pp.17~22 (2016)
  6. I. Gutman, "The energy of a graph", Ber. Math.-Statist. Sekt. Forschungsz. Graz, 103, pp.1~22 (1978)
  7. I. Gutman, "Algebraic Combinatorics and Applications", pp.196~211 (2001), Springer
  8. I. Gutman, "On the energy of regular graphs", MATCH Commun. Math, Comput. Chem., 57, pp.435~442 (2007)
  9. F. Harary, "Graph Theory" (1972), Addison Wesley
  10. I. N. Herstein, "Topics in Algebra" (2003), John Wiley & Sons
  11. V. Lokesha, "Skew-Zagreb Energy of Directed Graphs", Proceedings of the Jangjeon Math. Soc., 23(4), pp.557~568 (2020)
  12. K. N Prakasha, "Partition Laplacian Energy of a Graph", Advn. Stud. Contemp. Math, 27(4), pp.477~494 (2017)
  13. K. N Prakasha, "Minimum Covering Randic energy of a graph", Kyungpook Mathematical Journal, 57(4), pp.701~709 (2017)
  14. K. N Prakasha, "Sum-Connectivity Energy of Graphs", Adv. Math. Sci. Appl, 28(1), pp.85~98 (2019)
  15. X. Ma, "The coprime graph of a group", Int. J. Group Theory, 3(3), pp.13~23 (2014)
  16. K. V. Madhusudhan, "Randic type Additive connectivity Energy of a Graph", Vladikavkaz Mathematical Journal, 21(2), pp.18~26 (2019)
  17. R. Rajendra, "On general order prime graph of a enite group", Proc. Jangjeon Math. Soc, 17(4), pp.641~644 (2014)
  18. R. Rajendra, "On general order prime graph of a enite group-II", Adv. Appl. Discrete Math, 17(4), pp.437~444 (2016)
  19. R. Rajendra, "A note on energy of order prime graph of a enite group", International Journal of Scientiec and Engineer-ing Research, 7(5), pp.15~16 (2016)
  20. R. Rajendra, "Set-Prime Graph of a Finite Group", Proc. Jangjeon Math. Soc, 22(3), pp.455~462 (2019)
  21. R. Rajendra, "Some Results on Order Prime Graphs and General Order Prime graphs", Proc. Jangjeon Math. Soc, 24(2), pp.223~230 (2021)
  22. R. Rajendra, "Arithmetic Function Graph of a Finite Group", Palestine Journal of Mathematics, 11(2), pp.488~495 (2022)
  23. M. Sattanathan, "An introduction to order prime graph", Int. J. Contemp. Math. Sciences, 10(4), pp.467~474 (2009)
  24. P. Siva Kota Reddy, "Inverse Sum Indeg Energy of a Graph", Advn. Stud. Contemp. Math, 31(1), pp.7~20 (2021)
  25. P. Siva Kota Reddy, "Randic Type Hadi Energy of a Graph", The Nepali Mathematical Sciences Report, 39(2), pp.95~105 (2022)

관련 논문AI추천

SOME RESULTS ON ORDER PRIME GRAPHS AND GENERAL ORDER PRIME GRAPHSP. SIVA KOTA REDDY, R. RAJENDRA장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2021 · 제24권 제2호ON THE SKEW ENERGY OF SOME UNITARY CAYLEY DIGRAPHSC. Adiga, D.D. Somashekara, H.N. Ramaswamy, Z. Khoshbakht장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제2호A note on prime graph of a finite ringH. Mangala Gowramma, P. S. Hemavathi, P.Siva Kota Reddy, R. RAJENDRA장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제3호Upper bounds for energy of a graphC. Adiga, R.K. Zaferani장전수학회 · Advanced Studies in Contemporary Mathematics2008 · 제16권 제2호Set-prime graph of a finite groupK. V. Madhusudhan, P.Siva Kota Reddy, R. RAJENDRA장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제3호Fibonacci Graph and its EnergiesAnitha N., Chandrashekar Adiga, Savitha H. C.장전수학회 · Advanced Studies in Contemporary Mathematics2021 · 제31권 제1호

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