The forcing vertex detour monophonic number of a graph
نویسندگان
چکیده
منابع مشابه
Edge-to-vertex Detour Monophonic Number of a Graph
For a connected graph G = (V,E) of order at least three, the monophonic distance dm(u, v) is the length of a longest u− v monophonic path in G. For subsets A and B of V , the monophonic distance dm(A,B) is defined as dm(A,B) = min{dm(x, y) : x ∈ A, y ∈ B}. A u− v path of length dm(A,B) is called an A−B detour monophonic path joining the sets A,B ⊆ V, where u ∈ A and v ∈ B. A set S ⊆ E is called...
متن کاملThe Forcing Edge-to-vertex Detour Number of a Graph
For two vertices u and v in a graph G = (V, E), the detour distance D (u, v) is the length of a longest u – v path in G. A u – v path of length D (u, v) is called a u – v detour. For subsets A and B of V, the detour distance D (A, B) is defined as D (A, B) = min {D (x, y) : x ∈ A, y ∈ B}. A u – v path of length D (A, B) is called an A – B detour joining the sets A, B V where u ∈ A and v ∈ B. A...
متن کاملThe connected forcing connected vertex detour number of a graph
For any vertex x in a connected graph G of order p ≥ 2, a set S of vertices of V is an x-detour set of G if each vertex v in G lies on an x-y detour for some element y in S. A connected x-detour set of G is an x-detour set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected x-detour set of G is the connected x-detour number of G and is denoted by cdx(...
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 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 ...
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ژورنال
عنوان ژورنال: AKCE International Journal of Graphs and Combinatorics
سال: 2016
ISSN: 0972-8600,2543-3474
DOI: 10.1016/j.akcej.2016.03.002