SOME RESULTS ON ORDER PRIME GRAPHS AND GENERAL ORDER PRIME GRAPHS
0
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
The order prime graph OP(Γ) of a nite group Γ is a graph with the vertex set V (OP(Γ)) = Γ and any two distinct vertices a and b are adjacent in OP(Γ) if and only if (o(a), o(b)) = 1. The general order prime graph GOP(Γ) of Γ is a graph with vertex set V (GOP(Γ)) = Γ and any two distinct vertices a and b are adjacent in GOP(Γ) if and only if (o(a), o(b)) = 1 or p, where p is a prime and p < n. In this paper, we discuss some results involving eigenvalues and energy of order prime graphs and general order prime graphs of nite groups. Further, we de ne the order prime graphs of a nite group Γ with respect to subsets(subgroups) of Γ and investigate some properties.
Abstract
The order prime graph OP(Γ) of a nite group Γ is a graph with the vertex set V (OP(Γ)) = Γ and any two distinct vertices a and b are adjacent in OP(Γ) if and only if (o(a), o(b)) = 1. The general order prime graph GOP(Γ) of Γ is a graph with vertex set V (GOP(Γ)) = Γ and any two distinct vertices a and b are adjacent in GOP(Γ) if and only if (o(a), o(b)) = 1 or p, where p is a prime and p < n. In this paper, we discuss some results involving eigenvalues and energy of order prime graphs and general order prime graphs of nite groups. Further, we de ne the order prime graphs of a nite group Γ with respect to subsets(subgroups) of Γ and investigate some properties.
참고문헌 (19)
- A. E. Brouwer, "Spectra of Graphs-Monograph" (2011), Springer
- D. M. Cvetkovic, "Spectra of Graphs" (1979), Academic Press
- R. Diestel, "Graph Theory, Graduate texts in Mathematics-Volume 173" (2006), Springer
- H. R. Dorbidi, "A note on the coprime graph of a group", Int. J. Group Theory, 5(4), pp.17~22 (2016)
- I. Gutman, "The energy of a graph", Ber. Math.-Statist. Sekt. Forschungsz. Graz, 103, pp.1~22 (1978)
- I. Gutman, "Algebraic Combinatorics and Applications", pp.196~211 (2001), Springer
- I. Gutman, "On the energy of regular graphs", MATCH Commun. Math, Comput. Chem., 57, pp.435~442 (2007)
- F. Harary, "Graph Theory" (1972), Addison Wesley
- I. N. Herstein, "Topics in Algebra" (2003), John Wiley & Sons
- J. H. Koolen, "Maximal energy graphs", Adv. Appl. Math., 26, pp.47~52 (2001)
- J. H. Koolen, "Maximal energy bipartite graphs", Graphs Combin, 19, pp.131~135 (2003)
- X. Ma, "The coprime graph of a group", Int. J. Group Theory, 3(3), pp.13~23 (2014)
- B. J. McClelland, "Properties of the latent roots of a matrix: The estimation of π-electron energies", J. chem. Phys., 54, pp.640~643 (1971)
- R. RAJENDRA, "On general order prime graph of a finite group", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 17(4), pp.641~644 (2014), 장전수학회
- R. Rajendra, "On general order prime graph of a finite group-II", Adv. Appl. Discrete Math., 17(4), pp.437~444 (2016)
- R. Rajendra, "A note on energy of order prime graph of a finite group", International Journal of Scientific and Engineering Research, 7(5), pp.15~16 (2016)
- R. RAJENDRA, "A note on prime graph of a finite ring", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 22(3), pp.415~426 (2019), 장전수학회
- R. RAJENDRA, "Set-prime graph of a finite group", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 22(3), pp.455~462 (2019), 장전수학회
- M. Sattanathan, "An Introduction to Order Prime Graph", Int. J. Con-temp. Math. Sciences, 10(4), pp.467~474 (2009)