Domination with respect to nondegenerate properties: vertex and edge removal

Title:

Domination with respect to nondegenerate properties: vertex and edge removal

Creator:

Samodivkin, Vladimir

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:2d83d8d6-b944-425d-b576-7f09e1b3a4e3
uuid:2d83d8d6-b944-425d-b576-7f09e1b3a4e3
doi:10.21136/MB.2013.143231

Subject:

dominating set, domination number, bondage number, additive graph property, hereditary graph property, and induced-hereditary graph property

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper we present results on changing and unchanging of the domination number with respect to the nondegenerate property P, denoted by γP (G), when a graph G is modified by deleting a vertex or deleting edges. A graph G is (γP (G), k)P -critical if γP (G − S) < γP (G) for any set S ( V (G) with |S| = k. Properties of (γP , k)P -critical graphs are studied. The plus bondage number with respect to the property P, denoted b + P (G), is the cardinality of the smallest set of edges U ⊆ E(G) such that γP (G − U) > γP (G). Some known results for ordinary domination and bondage numbers are extended to γP (G) and b + P (G). Conjectures concerning b + P (G) are posed.

Language:

English

Rights:

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

Coverage:

75-85

Source:

Mathematica bohemica | 2013 Volume:138 | Number:1

Harvested from:

CDK

Metadata only:

false