On graphs whose local subgraphs are strongly regular with parameters \((144, 39, 6, 12)\)
type: Item
instance of: scholarly article
title: On graphs whose local subgraphs are strongly regular with parameters \((144, 39, 6, 12)\)
zbMATH Open document ID: 1304.05156
DOI: 10.1134/S1064562414020343
published in: Doklady Mathematics
publication date: 2014-10-15T00:00:00Z
review text: A graph \(\Gamma\) is called an edge-regular graph with parameters \((v, k, \lambda)\) if it is a regular graph of degree \(k\) on \(v\) vertices and each of its edges lies in \(\lambda\) triangles, and it is called an amply regular graph with parameters \((v, k, \lambda, \mu)\) if it is an edge-regular graph with the corresponding parameters and any two vertices \(a,b\) of \(\Gamma\) such that their distance \(d(a,b)=2\) have exactly \(\mu\) common neighbors. As a consequence of two theorems in this paper concerning amply regular graphs whose local subgraphs are strongly regular graphs with parameters \((144,39,6,12)\), the following corollary is deduced: Let \(\Gamma\) be an amply regular graph whose local subgraphs are strongly regular graphs with parameters \((144, 39, 6, 12)\). Then the following assertions hold: (1) \(\Gamma\) is not a distance-regular graph; (2) \(\Gamma\) is not a locally \(\Delta\)-graph, where \(\Delta\) is a known strongly regular graph with parameters \((144, 39, 6, 12)\) and automorphism group \(\mathrm{SL}_{3}(3)\).
reviewed by: Ioan Tomescu
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05C60
zbMATH DE Number: 6355658
zbMATH Keywords: strongly regular graph
zbMATH Keywords: edge-regular graph
zbMATH Keywords: amply regular graph
zbMATH Keywords: automorphism group
author: Alexandre A. Makhnev
author: Dmitriĭ Viktorovich Paduchikh
MaRDI profile type: Publication
cites work: On strongly regular graphs with eigenvalue 3 and their extensions
cites work: Q4209054
cites work: The Gewirtz graph: An exercise in the theory of graph spectra
cites work: Q3992965
description: scientific article; zbMATH DE number 6355658