On strongly regular graphs with b 1 < 24

2013 ◽  
Vol 283 (S1) ◽  
pp. 111-118
Author(s):  
M. S. Nirova
Keyword(s):  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Strongly Regular

On extensions of small strongly regular graphs with eigenvalue 3

2015 ◽  
Vol 92 (1) ◽  
pp. 482-486
Author(s):  
A. A. Makhnev ◽  
D. V. Paduchikh
Keyword(s):  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Strongly Regular

On triple systems and strongly regular graphs

2012 ◽  
Vol 119 (7) ◽  
pp. 1414-1426 ◽  
Author(s):  
Majid Behbahani ◽  
Clement Lam ◽  
Patric R.J. Östergård
Keyword(s):  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Triple Systems ◽  
Strongly Regular

On the Extendability of Quasi-Strongly Regular Graphs with Diameter 2

2018 ◽  
Vol 34 (4) ◽  
pp. 711-726 ◽  
Author(s):  
Hermina Alajbegović ◽  
Almir Huskanović ◽  
Štefko Miklavič ◽  
Primož Šparl
Keyword(s):  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Strongly Regular

scholarly journals Extension of Strongly Regular Graphs

10.37236/878 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Ralucca Gera ◽  
Jian Shen
Keyword(s):  
Positive Integer ◽  
Nonnegative Integer ◽  
Regularity Property ◽  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Strongly Regular ◽  
Vertex Degrees

The Friendship Theorem states that if any two people in a party have exactly one common friend, then there exists a politician who is a friend of everybody. In this paper, we generalize the Friendship Theorem. Let $\lambda$ be any nonnegative integer and $\mu$ be any positive integer. Suppose each pair of friends have exactly $\lambda$ common friends and each pair of strangers have exactly $\mu$ common friends in a party. The corresponding graph is a generalization of strongly regular graphs obtained by relaxing the regularity property on vertex degrees. We prove that either everyone has exactly the same number of friends or there exists a politician who is a friend of everybody. As an immediate consequence, this implies a recent conjecture by Limaye et. al.

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