The study of Roman domination number
| Autor: | Zhi-Xiong Xu, 許智雄 |
|---|---|
| Rok vydání: | 2014 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 102 Given a graph G = (V, E). We define a function f from V to {0, 1, 2}. The function f is called a Roman dominating function on G when satisfying the condition that every vertex v_i with f(v_i)=0 must be adjacent to at least one vertex v_j with f(v_j)=2. The weight of Roman dominating function f is the sum of the weight of each vertex of G. The minimum weight of all possible Roman dominating functions on G is the Roman domination number of G, denoted by γ_R (G). A spider graph G(k_1,k_2,k_3,…,k_t ) is the union of t paths〖 P〗_(k_1 ), 〖 P〗_(k_2 ), …, 〖 P〗_(k_t )with one common end vertex. A generalized spider graph〖 C〗_t (k_1,k_2,k_3,…,k_t ) is the union of a t-cycle〖 C〗_t=(1,2,3,…,t) and t paths〖 P〗_(k_1 ), 〖 P〗_(k_2 ), …, 〖 P〗_(k_t ) where each path intersect Ct with exact one vertex and〖 P〗_(k_i ) intersect Ct at the vertex i. In this thesis, we obtain the formula to calculate the minimum domination number and Roman domination number of each spider graph. For the Roman domination number of a generalized spider graph, we obtain the formula of γ_R (C_3 (k_(1 ), k_2, k_3 )) and γ_R (C_4 (k_1,k_2,k_3,k_4 )) related to the Roman domination number of a spider graph. After that we give two conjectures about calculating γ_R (C_5 (n_1,n_2,n_3,n_4,n_5 )) and γ_R (C_6 (n_1,n_2,n_3,n_4,n_5,n_6 )). |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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