Document Type

Article

Journal/Book Title/Conference

International Journal of Computer Mathematics: Computer Systems Theory

Publisher

Taylor & Francis

Publication Date

6-23-2020

First Page

1

Last Page

13

Abstract

Given a bipartite graph G = (X, Y, E), the bipartite dot product representation of G is a function f : X ∪Y → ℝk and a positive threshold t such that for any x ∈ X and y ∈ Y , xy ∈ E if and only if f(x) · f(y) ≥ t. The minimum k such that a bipartite dot product representation exists for G is the bipartite dot product dimension of G, denoted bdp(G). We will show that such representations exist for all bipartite graphs as well as give an upper bound for the bipartite dot product dimension of any graph. We will also characterize the bipartite graphs of bipartite dot product dimension 1 by their forbidden subgraphs.

Comments

This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Computer Mathematics: Computer Systems Theory on June 23, 2020, available online: https://doi.org/10.1080/23799927.2020.1779820.

Available for download on Wednesday, June 23, 2021

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