#### Title

### Isomorphism criterion for monomial graphs

#### Document Type

Article

#### Publication Date

1-1-2005

#### Abstract

Let q be a prime power, double-struck F signq be the field of q elements, and k, m be positive integers. A bipartite graph G = Gq(k, m) is defined as follows. The vertex set of G is a union of two copies P and L of two-dimensional vector spaces over double-struck F signq, with two vertices (p1, p2) ∈ P and [l1, l 2] ∈ L being adjacent if and only if p2 + l 2 = p1kl1m We prove that graphs Gq(k, m) and Gq′(k′, m′) are isomorphic if and only if q = q′ and {gcd(k, q - 1), gcd(m, q - 1)} = {gcd(k′, q - 1), gcd(m′, q - 1)} as multisets. The proof is based on counting the number of complete bipartite subgraphs in the graphs. © 2005 Wiley Periodicals, Inc.

#### Publication Title

Journal of Graph Theory

#### First Page Number

322

#### Last Page Number

328

#### DOI

10.1002/jgt.20055

#### Recommended Citation

Dmytrenko, Vasyl; Lazebnik, Felix; and Viglione, Raymond, "Isomorphism criterion for monomial graphs" (2005). *Kean Publications*. 2637.

https://digitalcommons.kean.edu/keanpublications/2637