A. R. Moghaddamfar, “About noncommuting graphs”, Sibirsk. Mat. Zh., 47:5 (2006), 1112–1116; Siberian Math. J., 47:5 (2006), 911

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Sibirskii Matematicheskii Zhurnal, 2006, Volume 47, Number 5, Pages 1112–1116 (Mi smj917)

This article is cited in 29 scientific papers (total in 29 papers)

About noncommuting graphs

A. R. Moghaddamfar

K. N. Toosi University of Technology

Full-text PDF (173 kB) Citations (29)

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Abstract: The noncommuting

\nabla (G)

$\nabla(G)$ of a nonabelian finite group

G

$G$ is defined as follows: The vertices of

\nabla (G)

$\nabla(G)$ are represented by the noncentral elements of

G

$G$ , and two distinct vertices

x

$x$ and

y

$y$ are joined by an edge if

x y \neq y x

$xy\ne yx$ . In [1], the following was conjectured: Let

G

$G$ and

H

$H$ be two nonabelian finite groups such that

\nabla (G) ≅ \nabla (H)

$\nabla(G)\cong\nabla(H)$ then

| G | = | H |

$|G|=|H|$ . Here we give some counterexamples to this conjecture.

Keywords: noncommuting graph, truncated skew-polynomial ring, group, Jacobson radical, regular graph.

Received: 02.08.2005

English version:
Siberian Mathematical Journal, 2006, Volume 47, Issue 5, Pages 911–914
DOI: https://doi.org/10.1007/s11202-006-0101-y

Bibliographic databases:

UDC: 519.542

Language: Russian

Citation: A. R. Moghaddamfar, “About noncommuting graphs”, Sibirsk. Mat. Zh., 47:5 (2006), 1112–1116; Siberian Math. J., 47:5 (2006), 911–914

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/smj917

https://www.mathnet.ru/eng/smj/v47/i5/p1112

This publication is cited in the following 29 articles:

M. Bahrami-Taghanaki, T. Foguel, A. R. Moghaddamfar, I. N. Nakaoka, J. Schmidt, “Nonstabilizing graphs arising from group actions”, Communications in Algebra, 2024, 1
Walaa Nabil Taha Fasfous, Rajat Kanti Nath, “Inequalities involving energy and Laplacian energy of non-commuting graphs of finite groups”, Indian J Pure Appl Math, 2023
Shi Wujie, “Quantitative characterization of finite simple groups”, Sci. Sin.-Math., 53:7 (2023), 931
Valentina Grazian, Carmine Monetta, “A conjecture related to the nilpotency of groups with isomorphic non-commuting graphs”, Journal of Algebra, 633 (2023), 389
Parthajit Bhowal, Deiborlang Nongsiang, Rajat Kanti Nath, “Non-Solvable Graphs of Groups”, Bull. Malays. Math. Sci. Soc., 45:3 (2022), 1255
J. C. M. Pezzott, “Double-toroidal and 1-planar non-commuting graph of a group”, ADM, 34:1 (2022), 132
Rezaie E., Ahmadidelir K., Tehranian A., Rasouli H., “Non-Commuting Graphs and Some Bounds For Commutativity Degree of Finite Moufang Loops”, Bull. Iran Math. Soc., 47:6 (2021), 1849–1869
Sharma M., Nath R.K., Shang Y., “On G-Noncommuting Graph of a Finite Group Relative to Its Subgroups”, Mathematics, 9:23 (2021), 3147
Muhie S.K., Otera D.E., Russo F.G., “Non-Permutability Graph of Subgroups”, Bull. Malays. Math. Sci. Soc., 44:6 (2021), 3875–3894
Mohammad A. Iranmanesh, Mohammad Hossein Zareian, “On n-centralizer CA-groups”, Communications in Algebra, 49:10 (2021), 4186
Bashir H.H., Ahmadidelir K., “Some Structural Graph Properties of the Non-Commuting Graph of a Class of Finite Moufang Loops”, Electron. J. Graph Theory Appl., 8:2 (2020), 319–337
Torktaz M., Ashrafi A.R., “Spectral Properties of the Commuting Graphs of Certain Groups”, AKCE Int. J. Graphs Comb., 16:3 (2019), 300–309
Jahandideh M., Modabernia R., Shokrolahi S., “Non-Commuting Graphs of Certain Almost Simple Groups”, Asian-Eur. J. Math., 12:5 (2019), 1950081
Mirzargar M., “a Survey on the Automorphism Groups of the Commuting Graphs and Power Graphs”, Facta Univ-Ser. Math. Informat., 34:4 (2019), 729–743
Ahmadidelir K., “On the Non-Commuting Graph in Finite Moufang Loops”, J. Algebra. Appl., 17:4 (2018), 1850070
Costa D., Davis V., Gill K., Hinkle G., Reid L., “Eulerian Properties of Non-Commuting and Non-Cyclic Graphs of Finite Groups”, Commun. Algebr., 46:6 (2018), 2659–2665
Nardulli S., Russo F.G., “Two Bounds on the Noncommuting Graph”, Open Math., 13 (2015), 273–282
B. R. Bakhadly, A. E. Guterman, O. V. Markova, “Graphs defined by orthogonality”, J. Math. Sci. (N. Y.), 207:5 (2015), 698–717
Leshchenko Yu.Yu., “on the Diameters of Commuting Graphs of Permutational Wreath Products”, Ukr. Math. J., 66:5 (2014), 732–742
Abdollahi A., Shahverdi H., “Non-Commuting Graphs of Nilpotent Groups”, Commun. Algebr., 42:9 (2014), 3944–3949

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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