Security in graphs
Abbreviated Journal Title
Discret Appl. Math.
alliances; defensive alliances; Mathematics, Applied
Let G = (V, E) be a graph. A set S subset of V is a defensive alliance if vertical bar N[x] boolean AND S vertical bar >= vertical bar N[x] - S vertical bar for every x epsilon S. Thus, each vertex of a defensive alliance can, with the aid of its neighbors in S, be defended from attack by its neighbors outside of S. An entire set S is secure if any subset X subset of S can be defended from an attack from outside of S, under an appropriate definition of what such a defense implies. Necessary and sufficient conditions for a set to be secure are determined. Published by Elsevier B.V.
Discrete Applied Mathematics
"Security in graphs" (2007). Faculty Bibliography 2000s. 6894.