Original Research Article

Article volume = 2023 and issue = 2

Pages: 127–131

Article publication Date: November 25, 2023

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On a Class of Symplectic Graphs and Their Automorphisms

Bahman Askari(a) and Fataneh Karimi(b)

(a) Department of Mathematics, Qorveh Branch, Islamic Azad University, Qorveh, Iran.

(b) Department of Mathematics, Shahre' Kord Branch, Islamic Azad University, Shahre' Kord, Iran.

Abstract:

It easy to see that each graph is a modification of a reduced graph Γ of the same rank. It is proved that for every reduced graph with binary rank 2r, there is a unique maximal graph with binary rank 2r which conatins Γ as an induced subgraph. These maximal graphs are called symplectic graphs. In this paper, we study the symplectic graphs which are defined over a ring. We also find the automorphism group of symplectic graphs which are defined over Zpn, where p is a prime number and n is positive integer.

Keywords:

Automorphism; Symplectic Graph; Symplectic Group; Generalized Symplectic Graph.

References:
  • [1] C. Godsil, G. Royal, Algebric graph theory, Speringer-Verlage New york (2001). 3
  • [2] B. Kirkwood, B.R. Mcdonald, R. P. Agarwal, The symplectic group over a ring with one in its stable range, Pacificy. Math., 92(1), (1981), 111–125. 1.1, 2, 2.4, 3, 3, 3
  • [3] Z. Liwei, C. Zhao, F. Rogcuan, M. Chagli, Full automorphism group of generalized symplectic graph, Sci. China Math, 56(7), (2013) 1509-1520. 1
  • [4] Y. Meemark, T. Prinyasart, On symplectic graphs modulo Pn, Discrete Math, 311(17), (2011) 1874–1878. 1.2, 3
  • [5] Z. Tang, Z. X. Wan, Symplectic graphs and their automorphisms, European J. Combin, 27(1), (2006) 38–50. 1, 3
Cite this article as:
  • Bahman Askari and Fataneh Karimi, On a Class of Symplectic Graphs and Their Automorphisms, Communications in Combinatorics, Cryptography & Computer Science, 2023(2), PP.127–131, 2023
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