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Strong Alliances in Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 1، دوره 4، شماره 1، شهریور 2019، صفحه 1-13 اصل مقاله (482.79 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2018.25921.1056 | ||
| نویسندگان | ||
| C. Hegde* 1؛ B. Sooryanarayana2 | ||
| 1Mangalore University | ||
| 2Dr. Ambedkar Institute of Technology | ||
| چکیده | ||
| For any simple connected graph $G=(V,E)$, a defensive alliance is a subset $S$ of $V$ satisfying the condition that every vertex $v\in S$ 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. | ||
| کلیدواژهها | ||
| Alliances؛ Defensive alliances؛ Secure sets؛ Strong alliances | ||
| مراجع | ||
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