%0 Journal Article
%T Strong Alliances in Graphs
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Hegde, C.
%A Sooryanarayana, B.
%D 2019
%\ 06/01/2019
%V 4
%N 1
%P 1-13
%! Strong Alliances in Graphs
%K Alliances
%K Defensive alliances
%K Secure sets
%K Strong alliances
%R 10.22049/cco.2018.25921.1056
%X For any simple connected graph $G=(V,E)$, a defensive alliance is a subset $S$ of $V$ satisfying the condition that every vertex $vin S$ has at most one more neighbour in $V-S$ than it has in $S$. The minimum cardinality of any defensive alliance in $G$ is called the alliance number of $G$, denoted $a(G)$. In this paper, we introduce a new type of alliance number called $k$-strong alliance number and its varieties. The bounds for 1-strong alliance number in terms of different graphical parameters are determined and the characterizations of graphs with 1-strong alliance number 1, 2, and $n$ are obtained.
%U http://comb-opt.azaruniv.ac.ir/article_13785_db97a57dfa7d3980c88f4ce8245a31b6.pdf