On the Neighborhood Alliance Sets in a Graph

B. Sooryanarayana, Silvia Leera Sequeira and M. Vishu Kumar

For any simple and connected graph ()()(),GVGEG=, a SV⊆is called a neighborhood set if []sSGNs∈≅, where []Nvdenotes the sub graph induced by the closed neighborhood []Nvof the vertex vin G. A defensive alliance is a non empty subset Sof Vsatisfying the condition that every vS∈has at most one more neighbor in VS−than it has in S. The minimum cardinality of any defensive alliance of Gis called the alliance number of G. A neighborhood set of Gwhich is also defensive alliance of Gis called a neighborhood alliance set, or simply anna−set. The minimum cardinality of an na−set is called neighborhood alliance number of G. Various types of na−sets are introduced in this article and minimum cardinality of each set in possible cases, is determined, for paths and cycles in particular.

Volume 11 | Issue 10

Pages: 66-74

DOI: 10.5373/JARDCS/V11I10/20193007