Distribution of global defensive k-alliances over some graph products

Mostafa Tavakoli () and Sandi Klavžar ()
Additional contact information
Mostafa Tavakoli: Ferdowsi University of Mashhad
Sandi Klavžar: University of Ljubljana

Central European Journal of Operations Research, 2019, vol. 27, issue 3, No 3, 615-623

Abstract: Abstract If $$G=(V_G, E_G)$$ G = ( V G , E G ) is a graph, then $$S\subseteq V_G$$ S ⊆ V G is a global defensive k-alliance in G if (i) each vertex not in S has a neighbor in S and (ii) each vertex of S has at least k more neighbors inside S than outside of it. The global defensive k-alliance number of G is the minimum cardinality among all global defensive k-alliance in G. In this paper this concept is studied on the generalized hierarchical, the lexicographic, the corona, and the edge corona product. For all of these products upper bounds expressed with related invariants of the factors are given. Sharpness of the bounds is also discussed.

Keywords: Global alliance; Global defensive k-alliance; Hierarchical product of graphs; Lexicographic product of graphs; 05C69; 05C76 (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10100-018-00605-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:cejnor:v:27:y:2019:i:3:d:10.1007_s10100-018-00605-w

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10100

DOI: 10.1007/s10100-018-00605-w

Access Statistics for this article

Central European Journal of Operations Research is currently edited by Ulrike Leopold-Wildburger

More articles in Central European Journal of Operations Research from Springer, Slovak Society for Operations Research, Hungarian Operational Research Society, Czech Society for Operations Research, Österr. Gesellschaft für Operations Research (ÖGOR), Slovenian Society Informatika - Section for Operational Research, Croatian Operational Research Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().