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#### Semitotal domination of some known trees

(International Mathematical Virtual Institute, 2021)

Let G = (V, E) be a graph without isolated vertices with vertex set V of order n = |V | and edge set E of size m = |E|. A vertex of a graph G is said to dominate itself and all its neighbors. A semitotal dominating set
in ...

#### Determination the importance of vertices in graph

(Technical University of Civil Engineering, 2020)

Betweenness is a good measure of the centrality of a vertex in a graph modeling social or communication network. Betweenness centrality is a measure of centrality in a graph based on shortest paths. For every pair of ...

#### Semitotal bondage number of certain graphs

(İKSAD Yayınevi, 2019)

A set S of vertices in a graph G with no isolated vertices is a semitotal dominating set, abbreviated STDset, of G if S is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal ...

#### Semitotal domination number of some graph operations

(John Wiley and Sons Inc, 2021)

A semitotal dominating set S (abbreviated semi-TD-set) of graph G = (V, E) is a subset such that S is a dominating set and each vertex in the S is within 2 distance from the another vertex of S. The semitotal domination ...

#### Semitotal domination of Harary graphs

(Tbilisi Centre for Mathematical Sciences, 2020)

Let G be a simple ﬁnite undirected and an isolate-free graph. A set S of vertices in G is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. ...