The forcing open monophonic number of a graph
نویسندگان
چکیده
منابع مشابه
The Open Monophonic Number of a Graph
For a connected graph G of order n, a subset S of vertices of G is a monophonic set of G if each vertex v in G lies on a x-y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is defined as the monophonic number of G, denoted by m(G). A monophonic set of cardinality m(G) is called a m–set of G. A set S of vertices of a connected graph G is an open m...
متن کاملThe vertex monophonic number of a graph
For a connected graph G of order p ≥ 2 and a vertex x of G, a set S ⊆ V (G) is an x-monophonic set of G if each vertex v ∈ V (G) lies on an x− y monophonic path for some element y in S. The minimum cardinality of an x-monophonic set of G is defined as the x-monophonic number of G, denoted by mx(G). An x-monophonic set of cardinality mx(G) is called a mx-set of G. We determine bounds for it and ...
متن کاملThe Connected Monophonic Number of a Graph
For a connected graph G = (V, E), a monophonic set of G is a set M � V (G) such that every vertex of G is contained in a monophonic path joining some pair of vertices in M. The monophonic number m (G) of G is the minimum order of its monophonic sets and any monophonic set of order m (G) is a minimum monophonic set of G. A connected monophonic set of a graph G is a monophonic set M such that the...
متن کاملForcing Total Detour Monophonic Sets in a Graph
For a connected graph G = (V,E) of order at least two, a total detour monophonic set of a graph G is a detour monophonic set S such that the subgraph induced by S has no isolated vertices. The minimum cardinality of a total detour monophonic set of G is the total detour monophonic number of G and is denoted by dmt(G). A subset T of a minimum total detour monophonic set S of G is a forcing total...
متن کاملThe Weak (Monophonic) Convexity Number of a Graph
Anstract. In a connected graph G a subset S of vertices of G is said to be a weak convex set if for any two vertices u , v of S , S contains all the vertices of a v u − shortest path in G . Maximum cardinality of a proper weak convex set of G is the weak convexity number of G denoted by ) (G wcon . Let the set ] , [ v u J consists of all those vertices lying on a v u − induced path in G . A sub...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proyecciones (Antofagasta)
سال: 2016
ISSN: 0716-0917
DOI: 10.4067/s0716-09172016000100005