Switched graphs of some strongly regular graphs related to the\n symplectic graph

2016/05/24 by Alice M. W. Hui, Hui, Alice M. W., B. G. Rodrigues +1
Computer Science · Mathematics · #05C50 #05E30 #51A50 #94B25 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1605.07400

openalex publication_date 2016/05/24 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Applying a method of Godsil and McKay citeGM to some graphs related to the\nsymplectic graph, a series of new infinite families of strongly regular graphs\nwith parameters\n(2ⁿ\±2^(n-1)/2,2^n-1\±2^(n-1)/2,2^n-2\±2^(n-3)/2,2^n-2\±2^(n-1)/2)\nare constructed for any odd n \≥ 5. The construction is described in terms\nof geometry of quadric in projective space. The binary linear codes of the\nswitched graphs are [2ⁿ \∓ 2^\(n-1)/(2),n+3,2^t+1]₂-code or [2ⁿ\n\∓ 2^\(n-1)/(2),n+3,2^t+2]₂-code.\n

Related

• Switched symplectic graphs and their 2-ranks
• Strongly regular graphs with the same parameters as the symplectic graph
• New families of strongly regular graphs
• Symplectic Graphs and Their Automorphisms
• New Strongly Regular Graphs from Finite Geometries via Switching