Foolproof Weak Roman Domination Problem

• Main Authors: Yung-Hsiang Cho, 卓永祥
• Other Authors: Yung-Ling Lai
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/31722270404352581676

碩士 === 國立嘉義大學 === 資訊工程學系研究所 === 103 === Abstract Given a graph G = (V,E) , a guard function f :V ®{0, 1, 2} of G decomposes the vertex set into 0 1 V , V , and 2 V such that { | ( ) } i V = v f v = i for 0 £ i £ 2 , and each 0 vÎV , 1 2 N(v)(V V ) ¹ Æ where N(v) ={u | uvÎE} . For a vertex 0 vÎV satisfies 1 2 uÎ N(v)(V V ) , a move function g( f :u ®v) respected to a guard function f is defined as g(v) =1, g(u) = f (u) -1, and g(w) = f (w) for wÎV -{u, v}. A foolproof weak Roman domination function (FWRDF) f of a graph G is a guard function such that for each 0 vÎV , every 1 2 uÎ N(v)(V V ) , the move function g( f :u ®v) is a guard function of G . The weight of a FWRDF is defined as 2 1 ( ) ( ) 2 | | | | v V w f f v V V Î = = + . The foolproof weak Roman domination number is the minimum weight of a FWRDF among all FWRDFs of G , denoted as * ( ) r g G . The weak Roman domination problem has been proved to be NP-Complete even with restriction to bipartite or chordal graphs. This thesis established the foolproof weak Roman domination problem on spider web graph, and cartesian product of a path with a cycle. Keywords: Foolproof weak Roman domination, spider web graph, Cartesian product graph.