Relations between $(\kappa,\tau)$-regular sets and star complements

Title:

Relations between $(\kappa,\tau)$-regular sets and star complements

Creator:

Anđelić, Milica, Cardoso, Domingos M., and Simić, Slobodan K.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8ca2ab94-8eb9-4460-ba4e-cda06e25cf07
uuid:8ca2ab94-8eb9-4460-ba4e-cda06e25cf07

Subject:

eigenvalue, star complement, non-main eigenvalue, and Hamiltonian graph

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $G$ be a finite graph with an eigenvalue $\mu $ of multiplicity $m$. A set $X$ of $m$ vertices in $G$ is called a star set for $\mu $ in $G$ if $\mu $ is not an eigenvalue of the star complement $G\setminus X$ which is the subgraph of $G$ induced by vertices not in $X$. A vertex subset of a graph is $(\kappa ,\tau )$-regular if it induces a $\kappa $-regular subgraph and every vertex not in the subset has $\tau $ neighbors in it. We investigate the graphs having a $(\kappa ,\tau )$-regular set which induces a star complement for some eigenvalue. A survey of known results is provided and new properties for these graphs are deduced. Several particular graphs where these properties stand out are presented as examples.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

73-90

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:1

Harvested from:

CDK

Metadata only:

false