한국전산응용수학회:학술대회논문집 (Proceedings of the Korean Society of Computational and Applied Mathematics Conference)
- 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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- Pages.16.1-16
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- 2003
The number of maximal independent sets of (k+1) -valent trees
초록
A subset S of vertices of a graph G is independent if no two vertices of S are adjacent by an edge in G. Also we say that S is maximal independent if it is contained In no larger independent set in G. A planted plane tree is a tree that is embedded in the plane and rooted at an end-vertex. A (k+1) -valent tree is a planted plane tree in which each vertex has degree one or (k+1). We classify maximal independent sets of (k+1) -valent trees into two groups, namely, type A and type B maximal independent sets and consider specific independent sets of these trees. We study relations among these three types of independent sets. Using the relations, we count the number of all maximal independent sets of (k+1) -valent trees with n vertices of degree (k+1).
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