Artículo
On the rank of the distance matrix of graphs
Fecha de publicación:
11/2022
Editorial:
Elsevier Science Inc.
Revista:
Applied Mathematics and Computation
ISSN:
0096-3003
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Let G be a connected graph with V(G)={v1,…,vn}. The (i,j)-entry of the distance matrix D(G) of G is the distance between vi and vj. In this article, using the well-known Ramsey's theorem, we prove that for each integer k≥2, there is a finite amount of graphs whose distance matrices have rank k. We exhibit the list of graphs with distance matrices of rank 2 and 3. Besides, we study the rank of the distance matrices of graphs belonging to a family of graphs with their diameters at most two, the trivially perfect graphs. We show that for each η≥1 there exists a trivially perfect graph with nullity η. We also show that for threshold graphs, which are a subfamily of the family of trivially perfect graphs, the nullity is bounded by one.
Palabras clave:
DISTANCE MATRIX
,
DISTANCE RANK
,
THRESHOLD GRAPH
,
TRIVIALLY PERFECT GRAPH
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Articulos(SEDE CENTRAL)
Articulos de SEDE CENTRAL
Articulos de SEDE CENTRAL
Citación
Dratman, Ezequiel; Grippo, Luciano Norberto; Moyano, Verónica Andrea; Pastine, Adrián Gabriel; On the rank of the distance matrix of graphs; Elsevier Science Inc.; Applied Mathematics and Computation; 433; 11-2022; 1-13
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