Classifying strongly regular graphs using lexical ordering of adjacency matrices
نویسندگان
چکیده
منابع مشابه
On the p-Rank of the Adjacency Matrices of Strongly Regular Graphs
Let F be a strongly regular graph with adjacency matrix A. Let I be the identity matrix, and J the all-1 matrix. Let p be a prime. Our aim is to study the p-rank (that is, the rank over Fp, the finite field with p elements) of the matrices M = aA + bJ + cI for integral a, b, c. This note is based on van Eijl [8]. 1. The Smith normal form Let us write M ~ N for integral matrices M and N of order...
متن کاملHadamard Matrices and Strongly Regular Graphs with the 3-e.c. Adjacency Property
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 \ 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...
متن کاملdeterminants of adjacency matrices of graphs
we study the set of all determinants of adjacency matrices of graphs with a given number of vertices. using brendan mckay's data base of small graphs, determinants of graphs with at most $9$ vertices are computed so that the number of non-isomorphic graphs with given vertices whose determinants are all equal to a number is exhibited in a table. using an idea of m. newman, it is proved that if $...
متن کاملGeneration of Strongly Regular Graphs from Normalized Hadamard Matrices
This paper proposes an algorithm which can be used to construct strongly regular graphs from Hadamard matrices.A graph is strongly regular if there are integers and such that every two adjacent vertices have common neighbours and every two non adjacent vertices have common neighbors. Proposed method is mainly based on basic matrix manipulations. If the order of the normalized Hadamard matr ix i...
متن کاملAn Example of Using Star Complements in Classifying Strongly Regular Graphs∗
In this paper we show how the star complement technique can be used to reprove the result of Wilbrink and Brouwer that the strongly regular graph with parameters (57, 14, 1, 4) does not exist.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1991
ISSN: 0898-1221
DOI: 10.1016/0898-1221(91)90076-g