Linear representation of a graph

Eduardo Montenegro; Eduardo Cabrera; José González Campos; Ronald Manríquez Peñafiel

doi:10.5269/bspm.v37i4.32949

Eduardo Montenegro Univerisdad de Playa Ancha Department of Mathematics and Statistics Laboratorio de investigación Lab[e]saM http://orcid.org/0000-0003-4561-0745
Eduardo Cabrera Univerisdad de Playa Ancha Department of Mathematics and Statistics Laboratorio de investigación Lab[e]saM
José González Campos Univerisdad de Playa Ancha Department of Mathematics and Statistics Laboratorio de investigación Lab[e]saM
Ronald Manríquez Peñafiel Univerisdad de Playa Ancha Department of Mathematics and Statistics Laboratorio de investigación Lab[e]saM

DOI: https://doi.org/10.5269/bspm.v37i4.32949

Keywords: Graph, Graphs, Abstract algebra

Abstract

In this paper the linear representation of a graph is defined. A linear representation of a graph is a subgroup of $GL(p,\mathbb{R})$, the group of invertible matrices of order $ p $ and real coefficients. It will be demonstrated that every graph admits a linear representation. In this paper, simple and finite graphs will be used, framed in the graphs theory's area

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