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Abstract

Vectors x=(x1,x2,...,xn)T and y=(y1,y2,...,yn)T are combinatorially orthogonal if |{i:xiyi≠0}|≠1. An undirected graph G=(V,E) is a combinatorially orthogonal graph if there exists f:V→ℝn such that for any u,vV, uvE 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 Pn.

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

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