scholarly journals A Block Negacyclic Bush-Type Hadamard Matrix and Two Strongly Regular Graphs

2002 ◽  
Vol 98 (1) ◽  
pp. 118-126 ◽  
Author(s):  
Zvonimir Janko ◽  
Hadi Kharaghani
Keyword(s):  
Hadamard Matrix ◽  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Strongly Regular

scholarly journals Hadamard Matrices and Strongly Regular Graphs with the $3$-e.c. Adjacency Property

10.37236/1545 ◽  
2000 ◽  
Vol 8 (1) ◽  
Author(s):  
Anthony Bonato ◽  
W. H. Holzmann ◽  
Hadi Kharaghani
Keyword(s):  
Hadamard Matrix ◽  
Infinite Family ◽  
Hadamard Matrices ◽  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Element Subset ◽  
Strongly Regular ◽  
Almost All ◽  
Paley Graphs

A graph is $3$-e.c. if for every $3$-element subset $S$ of the vertices, and for every subset $T$ of $S$, there is a vertex not in $S$ which is joined to every vertex in $T$ and to no vertex in $S\setminus T$. Although almost all graphs are $3$-e.c., the only known examples of strongly regular $3$-e.c. graphs are Paley graphs with at least $29$ vertices. We construct a new infinite family of $3$-e.c. graphs, based on certain Hadamard matrices, that are strongly regular but not Paley graphs. Specifically, we show that Bush-type Hadamard matrices of order $16n^2$ give rise to strongly regular $3$-e.c. graphs, for each odd $n$ for which $4n$ is the order of a Hadamard matrix.

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
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