On the nullspace of arc-transitive graphs over finite fields

被引：3

作者：

Potocnik, Primoz ^{[2
,3
]}

Spiga, Pablo ^{[1
]}

Verret, Gabriel ^{[3
]}

机构：

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy

[2] Univ Ljubljana, Fac Math & Phys, Ljubljana, Slovenia

[3] Inst Math Phys & Mech, Ljubljana 1000, Slovenia

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2012年 / 36卷 / 03期

关键词：

Arc-transitive graphs; Graph-restrictive groups; Spectral graph theory; Finite fields;

D O I：

10.1007/s10801-011-0340-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be the adjacency matrix of a graph I". The nullity of A (that is, the dimension of the nullspace of A), when viewed as a matrix over a field of prime characteristic p, is called the p-nullity of I". We present several families of arc-transitive graphs with arbitrarily large p-nullity. We also show that the p-nullity of a vertex-transitive graph of order a power of p is zero, provided that the valency of the graph is coprime to p.

引用

页码：389 / 401

页数：13

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