期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2016
卷号：13
期号：1
页码：76-84
DOI：10.1016/j.akcej.2016.03.002
语种：English
出版社：Elsevier
摘要：Abstract For any two vertices x and y in a connected graph G , an x – y path is a monophonic path if it contains no chord, and a longest x – y monophonic path is called an x – y detour monophonic path. For any vertex x in G , a set S x ⊆ V ( G ) is an x -detour monophonic set of G if each vertex v ∈ V ( G ) lies on an x – y detour monophonic path for some element y in S x . The minimum cardinality of an x -detour monophonic set of G is the x -detour monophonic number of G , denoted by d m x ( G ) . A subset T x of a minimum x -detour monophonic set S x of G is an x -forcing subset for S x if S x is the unique minimum x -detour monophonic set containing T x . An x -forcing subset for S x of minimum cardinality is a minimum x -forcing subset of S x . The forcing x -detour monophonic number of S x , denoted by f d m x ( S x ) , is the cardinality of a minimum x -forcing subset for S x . The forcing x -detour number of G is f d m x ( G ) = min { f d m x ( S x ) } , where the minimum is taken over all minimum x -detour monophonic sets S x in G . We determine bounds for it and find the same for some special classes of graphs. Also we show that for every pair s , t of integers with 2 ≤ s ≤ t , there exists a connected graph G such that f d m x ( G ) = s and d m x ( G ) = t for some vertex x in G .
关键词：KeywordsenDetour monophonic pathVertex detour monophonic numberForcing vertex detour monophonic number
