scholarly journals Cyclic arcs of Singer type and strongly regular Cayley graphs over finite fields

2022 ◽  
Vol 77 ◽  
pp. 101953
Author(s):  
Koji Momihara ◽  
Qing Xiang
Keyword(s):  
Finite Fields ◽  
Cayley Graphs ◽  
Strongly Regular

scholarly journals Directed strongly regular Cayley graphs on dihedral groups

2021 ◽  
Vol 391 ◽  
pp. 125651
Author(s):  
Yiqin He ◽  
Bicheng Zhang ◽  
Rongquan Feng
Keyword(s):  
Cayley Graphs ◽  
Dihedral Groups ◽  
Strongly Regular

scholarly journals Strongly regular Cayley graphs with λ − μ = −1

1994 ◽  
Vol 67 (1) ◽  
pp. 116-125 ◽  
Author(s):  
K.T Arasu ◽  
D Jungnickel ◽  
S.L Ma ◽  
A Pott
Keyword(s):  
Cayley Graphs ◽  
Strongly Regular

scholarly journals Directed Strongly Regular Cayley Graphs over Metacyclic Groups of Order 4n

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1011 ◽  
Author(s):  
Tao Cheng ◽  
Lihua Feng ◽  
Weijun Liu
Keyword(s):  
Positive Integer ◽  
Cayley Graphs ◽  
Metacyclic Group ◽  
Metacyclic Groups ◽  
Strongly Regular

We construct several new families of directed strongly regular Cayley graphs (DSRCGs) over the metacyclic group M 4 n = ⟨ a , b | a n = b 4 = 1 , b − 1 a b = a − 1 ⟩ , some of which generalize those earlier constructions. For a prime p and a positive integer α > 1 , for some cases, we characterize the DSRCGs over M 4 p α .

Certain 3-decompositions of complete graphs, with an application to finite fields

1985 ◽  
Vol 99 (3-4) ◽  
pp. 277-281 ◽  
Author(s):  
Peter Rowlinson
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Complete Graph ◽  
Disjoint Union ◽  
Necessary Condition ◽  
Complete Graphs ◽  
Characteristic P ◽  
Strongly Regular

SynopsisA necessary condition is obtained for a complete graph to have a decomposition as the line-disjoint union of three isomorphic strongly regular subgraphs. The condition is used to determine the number of non-trivial solutions of the equation x3+y3 = z3 in a finite field of characteristic p ≡ 2 mod 3.

scholarly journals Integral Cayley Graphs Generated by Distance Sets in Vector Spaces over Finite Fields

10.37236/2730 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Ngoc Dai Nguyen ◽  
Minh Hai Nguyen ◽  
Duy Hieu Do ◽  
Anh Vinh Le
Keyword(s):  
Finite Fields ◽  
Euclidean Distance ◽  
Cayley Graphs ◽  
Vector Spaces ◽  
Sufficient Condition ◽  
Finite Rings ◽  
Distance Sets

Si Li and the fourth listed author (2008) considered unitary graphs attached to the vector spaces over finite rings using an analogue of the Euclidean distance. These graphs are shown to be integral when the cardinality of the ring is odd or the dimension is even. In this paper, we show that the statement also holds for the remaining case: the cardinality of the ring is even and the dimension is odd, by showing a sufficient condition for Cayley graphs generated by distance sets in vector spaces over finite fields to be integral.

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