TY - JOUR

T1 - Minimum rank and path cover number for generalized and double generalized cycle star graphs

AU - Perdigão, Cecília

AU - Fonseca, Amélia

N1 - info:eu-repo/grantAgreement/FCT/5876/147204/PT#
info:eu-repo/grantAgreement/FCT/5876/147208/PT#
This work was partially supported by the "Fundacao para a Ciencia e Tecnologia" (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes).
This work was partially supported by the "Fundacao para a Ciencia e Tecnologia" (Portuguese Foundation for Science and Technology) through the project UID/MAT/04721/2013 (Centro de Analise Funcional e Estruturas Lineares).

PY - 2018/10/1

Y1 - 2018/10/1

N2 - For a given connected (undirected) graph G=(V,E), with V={1,…,n}, the minimum rank of G is defined to be the smallest possible rank over all symmetric matrices A=[aij] such that for i≠j, aij=0 if, and only if, {i,j}∉E. The path cover number of G is the minimum number of vertex-disjoint paths occurring as induced subgraphs of G that cover all the vertices of G. When G is a tree, the values of the minimum rank and of the path cover number are known as well the relationship between them. We study these values and their relationship for all graphs that have at most two vertices of degree greater than two: generalized cycle stars and double generalized cycle stars.

AB - For a given connected (undirected) graph G=(V,E), with V={1,…,n}, the minimum rank of G is defined to be the smallest possible rank over all symmetric matrices A=[aij] such that for i≠j, aij=0 if, and only if, {i,j}∉E. The path cover number of G is the minimum number of vertex-disjoint paths occurring as induced subgraphs of G that cover all the vertices of G. When G is a tree, the values of the minimum rank and of the path cover number are known as well the relationship between them. We study these values and their relationship for all graphs that have at most two vertices of degree greater than two: generalized cycle stars and double generalized cycle stars.

KW - Cycle

KW - Double generalized cycle star

KW - Generalized cycle star

KW - Generalized star

KW - Graphs

KW - Maximum multiplicity

KW - Minimum rank

KW - Path cover number

KW - Symmetric matrices

UR - http://www.scopus.com/inward/record.url?scp=85047871391&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2018.05.016

DO - 10.1016/j.laa.2018.05.016

M3 - Article

AN - SCOPUS:85047871391

VL - 554

SP - 146

EP - 169

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -