The forcing connected detour number of a graph
نویسندگان
چکیده
منابع مشابه
The 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 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 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 detour 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-detour set of G if each vertex v ∈ V(G) lies on an x − y detour for some element y in S. The minimum cardinality of an xdetour set of G is defined as the x-detour number of G, denoted by dx(G). An x-detour set of cardinality dx(G) is called a dx-set of G. A connected x-detour set of G is an x-detour set S such th...
متن کاملCharacterizations of the Connected Forcing Number of a Graph
Zero forcing is a dynamic graph coloring process whereby a colored vertex with a single uncolored neighbor forces that neighbor to be colored. This forcing process has been used to approximate certain linear algebraic parameters, as well as to model the spread of diseases and information in social networks. In this paper, we introduce and study the connected forcing process – a restriction of z...
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ژورنال
عنوان ژورنال: Proyecciones (Antofagasta)
سال: 2014
ISSN: 0716-0917
DOI: 10.4067/s0716-09172014000200002