Domination in generalized Petersen graphs.

• Main Authors: Yuan-shin Li, 李元馨
• Other Authors: Sheng-Chyang Liaw
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/25053155376826226509

碩士 === 國立中央大學 === 數學研究所 === 99 === A vertex subset S of a graph G is a dominating set if each vertex in V(G)−S is adjacent to at least one vertex in S. The domination number of G is the cardinality of a minimum dominating set of G, denoted by γ(G). A dominating set S is called an independent dominating set if S is also an independent set. The independent domination number of G is the cardinality of a minimum independent dominating set of G, denoted by γi(G). A dominating set S is called a total dominating set if each vertex v of G is dominated by some vertex u , v of S. The total domination number of G is the cardinality of a minimum total dominating set of G, denoted by γt(G). In a generalized Petersen graph P(n, k), its vertex set should be the union of V = {v1, v2, ..., vn} and U = {u1, u2, ..., un}, and its edge set be the union of {vivi+1, viui, uiui+k} which all the subscripts are under addition modulo n and 1 ≤k ≤ ⌊n2⌋. In [3], [4], and [5], the exact values of γ(P(2k + 1, k)), γ(P(n, 1)), γ(P(n, 2)),γt(P(n, 2)), and γ(P(n, 3)) are determined. In this thesis, we will determine the exact values of γi(P(2k+1, k)), γt(P(2k+1, k)), γ(P(2k, k)), γi(P(2k, k)), and γt(P(2k, k))in Section 2. In Section 3, we find the exact values of γi(P(n, 1)), γt(P(n, 1)), and γi(P(n, 2)). We give the exact value of γi(P(n, 3)) and a lower bound and an upperbound for γt(P(n, 3)) in Section 4.