The forcing total restrained geodetic number and the total restrained geodetic number of a graph: Realizability and complexity
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چکیده
منابع مشابه
The Restrained Edge Geodetic Number of a Graph
A set S of vertices of a connected graph G is a geodetic set if every vertex of G lies on an x−y geodesic for some elements x and y in S. The minimum cardinality of a geodetic set ofG is the geodetic number ofG, denoted by g(G). A set S of vertices of a graph G is an edge geodetic set if every edge of G lies on an x − y geodesic for some elements x and y in S. The minimum cardinality of an edge...
متن کاملThe forcing geodetic number of a graph
For two vertices u and v of a graph G, the set I(u, v) consists of all vertices lying on some u − v geodesic in G. If S is a set of vertices of G, then I(S) is the union of all sets I(u, v) for u, v ∈ S. A set S is a geodetic set if I(S) = V (G). A minimum geodetic set is a geodetic set of minimum cardinality and this cardinality is the geodetic number g(G). A subset T of a minimum geodetic set...
متن کاملThe Upper Edge Geodetic Number and the Forcing Edge Geodetic Number of a Graph
An edge geodetic set of a connected graph G of order p ≥ 2 is a set S ⊆ V (G) such that every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g1(G) of G is the minimum cardinality of its edge geodetic sets and any edge geodetic set of cardinality g1(G) is a minimum edge geodetic set of G or an edge geodetic basis of G. An edge geodetic set S in ...
متن کاملBounds on the restrained Roman domination number of a graph
A {em Roman dominating function} on a graph $G$ is a function$f:V(G)rightarrow {0,1,2}$ satisfying the condition that everyvertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex$v$ for which $f(v) =2$. {color{blue}A {em restrained Roman dominating}function} $f$ is a {color{blue} Roman dominating function if the vertices with label 0 inducea subgraph with no isolated vertex.} The wei...
متن کاملThe Total Restrained Monophonic Number of a Graph
For a connected graph G = (V,E) of order at least two, a total restrained monophonic set S of a graph G is a restrained monophonic set S such that the subgraph induced by S has no isolated vertices. The minimum cardinality of a total restrained monophonic set of G is the total restrained monophonic number of G and is denoted by mtr(G). A total restrained monophonic set of cardinality mtr(G) is ...
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ژورنال
عنوان ژورنال: AKCE International Journal of Graphs and Combinatorics
سال: 2017
ISSN: 0972-8600,2543-3474
DOI: 10.1016/j.akcej.2017.03.007