### Title page for etd-0728105-104156

URN etd-0728105-104156 Pei-lan Yen yenpl@math.nsysu.edu.tw This thesis had been viewed 5217 times. Download 1847 times. Applied Mathematics 2004 2 Master English The Convexity Spectra and the Strong Convexity Spectra of Graphs 2005-05-27 26 Convex set convexity number convexity spectrum complete graph Given a connected oriented graph D, we say that a subset S of V(D) is convex in D if, for every pair of vertices x, y in S, the vertex set of every x-y geodesic (x-y shortest dipath) and y-x geodesic in D is contained in S. The convexity number con (D) of a nontrivial connected oriented graph D is the maximum cardinality of a proper convex set of D. Let S_{C}(K_{n})={con(D)|D is an orientation of K_{n}} and S_{SC}(K_{n})={con(D)|D is a strong orientation of K_{n}}. We show that S_{C}(K_{3})={1,2} and S_{C}(K_{n})={1,3,4,...,n-1} if n >= 4. We also have that S_{SC}(K_{3})={1} and S_{SC}(K_{n})={1,3,4,...,n-2} if n >= 4 .We also show that every triple n, m, k of integers with n >= 5, 3 <= k <= n-2, and n+1 <= m <= n(n-1)/2, there exists a strong connected oriented graph D of order n with |E(D)|=m and con (D)=k. Xuding Zhu - chair Sen-Peng Eu - co-chair Tsai-Lien Wong - co-chair Li-Da Tong - advisor indicate access worldwide 2005-07-28

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