Combinatorially Orthogonal Paths

Authors

Sean A. Bailey, Texas A&M University TexarkanaFollow
David E. Brown, Utah State UniversityFollow
Leroy Beaseley, Utah State UniversityFollow

DOI Link

https://doi.org/10.70013/l1vy8zr6

Abstract

Vectors x=(x₁,x₂,...,x_n)^T and y=(y₁,y₂,...,y_n)^T are combinatorially orthogonal if |{i:x_iy_i≠0}|≠1. An undirected graph G=(V,E) is a combinatorially orthogonal graph if there exists f:V→ℝⁿ such that for any u,v∈V, uv∉E iff f(u) and f(v) are combinatorially orthogonal. We will show that every graph has a combinatorially orthogonal representation. We will show the bounds for the combinatorially orthogonal dimension of any path P_n.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

Bailey, Sean A.; Brown, David E.; and Beaseley, Leroy (2023) "Combinatorially Orthogonal Paths," Communications on Number Theory and Combinatorial Theory: Vol. 4, Article 2.
DOI: 10.70013/l1vy8zr6
Available at: https://research.library.kutztown.edu/contact/vol4/iss1/2