Connected edge monophonic number of a graph
نویسندگان
چکیده
منابع مشابه
The 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 کاملThe Connected Detour Monophonic Number of a Graph
For a connected graph G = (V,E) of order at least two, a chord of a path P is an edge joining two non-adjacent vertices of P . A path P is called a monophonic path if it is a chordless path. A longest x− y monophonic path is called an x− y detour monophonic path. A set S of vertices of G is a detour monophonic set of G if each vertex v of G lies on an x − y detour monophonic path, for some x an...
متن کاملThe Connected 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). A connected x-monophonic set of G is an x-monophonic set S such that the subgraphG[S] induced by ...
متن کاملUpper Edge Detour Monophonic Number of a Graph
For a connected graph G of order at least two, a path P is called a monophonic path if it is a chordless path. A longest x−y monophonic path is called an x − y detour monophonic path. A set S of vertices of G is an edge detour monophonic set of G if every edge of G lies on a detour monophonic path joining some pair of vertices in S. The edge detour monophonic number of G is the minimum cardinal...
متن کاملEdge-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...
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ژورنال
عنوان ژورنال: Proyecciones (Antofagasta)
سال: 2013
ISSN: 0716-0917
DOI: 10.4067/s0716-09172013000300002