دانشگاه گیلان
معاونت پژوهش و فناوری دانشگاه گیلان
انتشارات دانشگاه گیلان

 آمار

تعداد نشریات31
تعداد شماره‌ها797
تعداد مقالات7,618
تعداد مشاهده مقاله29,111,052
تعداد دریافت فایل اصل مقاله7,672,316
Amreen, J., Naduvath, S.. (1403). Order sum signed graph of a group. فیزیولوژی و بیوتکنولوژی آبزیان, 12(2), 87-98. doi: 10.22124/jart.2024.23574.1488
J. Amreen; S. Naduvath. "Order sum signed graph of a group". فیزیولوژی و بیوتکنولوژی آبزیان, 12, 2, 1403, 87-98. doi: 10.22124/jart.2024.23574.1488
Amreen, J., Naduvath, S.. (1403). 'Order sum signed graph of a group', فیزیولوژی و بیوتکنولوژی آبزیان, 12(2), pp. 87-98. doi: 10.22124/jart.2024.23574.1488
Amreen, J., Naduvath, S.. Order sum signed graph of a group. فیزیولوژی و بیوتکنولوژی آبزیان, 1403; 12(2): 87-98. doi: 10.22124/jart.2024.23574.1488

Order sum signed graph of a group

Journal of Algebra and Related Topics
دوره 12، شماره 2، فروردین 2025، صفحه 87-98    اصل مقاله (283.25 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22124/jart.2024.23574.1488
نویسندگان
J. Amreen؛ S. Naduvath*
Department of Mathematics, Christ University, Bangalore, India
چکیده
The order sum graph associated with the group $G$, denoted by $\Gamma_{os}$, is a graph with vertex set consisting of elements of $G$ and two vertices say $a$,$b$ $\in \Gamma_{os}$ are adjacent if $o(a)+o(b)>o(G)$, where $o(\ast)$ denotes the order of a group or an element of a group. In this paper, we introduce a signed graph called order sum signed graph where the underlying graph is a complete graph of order $n$ and the edges receive positive and negative signs based on the order sum graph. We characterise the balanced negated order sum signed graphs. We also characterise the positive and negative homogeneous order sum signed graphs. Further, we study the properties such as clusterability, sign-compatibility, consistency and switching of signed graphs. Further, we obtain the adjacency spectra, Laplacian spectra and signless Laplacian spectra of the order sum signed graphs associated with cyclic groups.
کلیدواژه‌ها
Algebraic graphs؛ order sum graphs؛ order sum signed graphs
مراجع
  1. A. Abdollahi, S. Akbari and H.R. Maimani, Non-commuting graph of a group, J. Algebra, (2) 298 (2006), 468-492.
  2.  A. Abdollahi and A.M. Hassanabadi, Noncyclic graph of a group, Commun. Algebra, (7) 35 (2007), 2057-2081.
  3.  S. Akbari, F. Heydari and M. Maghasedi, The intersection graph of a group, J. Algebra Appl., (5) 14 (2015), 1550065.
  4.  M.R. Alfuraidan and Y.F. Zakariya, Inverse graphs associated with nite groups, Electron. J. Graph Theory Appl., (1) 5 (2017), 55570.
  5. J. Amreen and S. Naduvath, On non-inverse graph of a group, Discuss. Math. Gen. Algebra Appl., (2) 42 (2022), 315-325.
  6.  J. Amreen, and Naduvath, S., Order sum graph of a group, Bagdhad Sci. J., (1) 20 (2023), 181-188.
  7. D. F. Anderson and A. BadawiThe total graph of a commutative ring, J. Algebra, (7) 320 (2008), 2706-2719.
  8. D. F. Anderson, J. Fasteen and J.D. LaGrange, The subgroup graph of a group, Arabian J. Math., (1) 1 (2012), 17-27.
  9.  D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, (2) 217 (1999), 434-447.
  10. P. Balakrishnan, M. Sattanathan and R. Kala, The center graph of a group, South Asian J. Math., 1 (2011), 21-28.
  11.  P. J. Cameron and S. Ghosh, The power graph of a  nite group, Discrete Math., (13) 311 (2011), 1220-1222.
  12.  E. Carnia, M. Suyudi, I. Aisah and A.K. Supriatna, A review on eigenvalues of adjacency matrix of graph with cliques, AIP Conf. Proc. 1868, (2017), 040001.
  13.  D. Cartwright and F. Harary, Structural balance: a generalization of Heider's theory, Psychol. Review, (5) 63 (1956), 277.
  14.  I. Chakrabarty, S. Ghosh, T.K. Mukherjee and M.K. Sen, Intersection graphs of ideals of rings, Discrete Math., (17) 309 (2009), 5381-5392.
  15. P. M. Cohn, Basic algebra: groups, rings and  elds. Springer Science and Business Media, 2012.
  16.  F. DeMeyer, and L. DeMeyer, Zero divisor graphs of semigroups, J. Algebra, (1) 283 (2005), 190-198.
  17.  E. Dobson, P. Spiga and V. Gabriel, Cayley graphs on abelian groups, Combinatorica, (4) 36 (2016), 371-393.
  18.  J. Dutta and R.K. Nath, Spectrum of commuting graphs of some classes of  nite groups, Mathematika, (1) 33 (2017), 87-95.
  19. J. B. Fraleigh, A  rst course in abstract algebra, Pearson Education, 2003.
  20.  F. Harary, On the notion of balance of a signed graph, Michigan Math. J., (2) 2 (1953), 143-146.
  21. T.W. Hungerford, Algebra, Springer Science and Business Media.
  22. B. L. Johnston and F. Richman, Numbers and Symmetry: An Introduction to Algebra, CRC Press, 1997.
  23. J. V. Kureethara, Hamiltonian cycle in complete multipartite graphs, Annal. Pure Appl. Math. (2) 13 (2017), 223-228.
  24. X. L. Ma, H.Q. Wei and G. Zhong, , The cyclic graph of a  nite group, Algebra, 2013 (2013), 107265.
  25. X. L. Ma, H.Q. Wei and L.Y. Yang, The coprime graph of a group , Int. J. Group Theory, (3) 3 (2014), 13-23.
  26.  P. Nasehpour, A generalization of zero-divisor graphs, J. Algorithms Comput., (2) 51 (2019), 35-45.
  27. S. K. Pundir, A competitive approach to modern algebra, CBS, 2015.
  28. E. Sampathkumar, Point signed and line signed graphs, Nat. Acad. Sci. Letters, (3) 7 (1984), 91-93.
  29. E. Sampathkumar, M.A. Sriraj and L. Pushpalatha, Notions of Balance in Signed and Marked Graphs, Indian J. Discrete Math., (1) 3 (2017), 25-32.
  30. P. Sharma and M. Acharya, Balanced signed total graphs of commutative rings, Graphs Combin., (4) 32 (2016), 1585-1597.
  31. D. Sinha and A. Dhama, Sign-compatibility of some derived signed graphs, Mapana J. Sci., (4) 11 (2012), 1-14
  32.  D. Sinha, D. Sharma, and B. Kaur, Signed zero-divisor graph, Electron. Notes. Discrete Math., 63 (2017), 517-524.
  33.  R. Suganya, and K. Nagarajan, Distance coprime graphs, Int. J. Pure Eng. Math., (1) 4 (2016), 19-30.
  34. E. B. Vinberg, A course in algebra, American Mathematical Soc., 2003.
  35. E. W. Weisstein, Clique Number, 2002, From MathWorld{A Wolfram Web Re-source, https://mathworld.wolfram.com/CliqueNumber.html.
  36. D. B. West, Introduction to graph theory, Upper Saddle River: Prentice hall, 2001.
  37. T. Zaslavsky, Signed graphs and geometry, J. Combin. Inform. System, 32 (2013), 1-32.
  38. T. Zaslavsky, Signed graphs, Discrete Appl. Math. (1) 4 (1982), 47-74.
آمار
تعداد مشاهده مقاله: 64
تعداد دریافت فایل اصل مقاله: 63


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب