Let G = (V (G), E(G)) be any finite, undirected, simple graph. The maximun size of a clique containing a vertex \(\mathit{x}\) \(\in\) V (G) is called the clique centrality of \(\mathit{x}\) , denoted by \(\omega\)G (\(\mathit{x}\)) . A set D \(\subseteq\) V (G) is said to be a p...
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Research Article10.9734/arjom/2023/v19i10722
Let G = (V (G),E (G)) be any finite, undirected, simple graph. The clique centrality of a vertex \(\mathit{x}\) \(\in\) V (G), denoted by \(\omega\)G (\(\mathit{x}\)), is the maximum size of a clique in G containing \(\mathit{x}\). A set D \(\subseteq\) V (G) is introduced in thi...
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Research Article10.9734/arjom/2023/v19i9717
Let G = (V (G), E(G)) be any finite, undirected, simple graph. A set D \(\subseteq\) V (G) is introduced in this paper as a clique-safe dominating set of G if D is a dominating set of G and for every clique D\(\prime\)m of size m in the subgraph induced by V (G) \D, there exists...
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Research Article10.9734/arjom/2023/v19i4651
A subset W \(\subseteq\) V (G) of a graph G is an independent semitotal dominating set of G, abbreviated ISTd-set of G, if W is an independent dominating set of G and every element of W is exactly of distance 2 from at least one other element of W. The independent semitotal domin...
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Research Article10.9734/arjom/2023/v19i3647
We formally introduce in this paper two parameters in graph theory, namely, clique centrality and global clique centrality. Let G be a finite, simple and undirected graph of order n. A clique in G is a nonempty subset W \(\subseteq\) V (G) such that the subgraph \(\langle\)W\(\ra...
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Research Article10.9734/arjom/2023/v19i2640
Remarl Joseph M. Damalerio, Rolito G. Eballe, Cherry Mae R. Balingit, Isagani S. Cabahug Jr. & Ann Leslie V. Flores·Asian Research Journal of Mathematics·2022
The global clustering coefficient is one of the most useful indices in complex network analysis. It is another metric that somehow measures how close a graph from being a complete graph. In this paper we present some expressions for the global clustering coefficient of the join G...
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Research Article10.9734/arjom/2022/v18i12632
Given a graph G = (V (G),E(G)), a nonempty set S \(\subseteq\) V (G) of fixed cardinality \(\gamma\)(G) - k is called a \(\zeta\)k - set of G, where 1 \(\le\) k \(\le\) \(\gamma\)(G) -1, if S gives the minimum cardinality |V (G) \ NG[S]| for all the possible subsets of V (G), eac...
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Research Article10.9734/arjom/2022/v18i12628
The global clustering Coefficient Cc(G) of a connected graph G of order at least 3 is a metric that somehow measures how close G to being a complete graph. Its value ranges from 0 to 1. In this paper, we will show that for the tensor product Km ⊗ Km and cartesian product Km ʘ Km ...
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Research Article10.9734/arjom/2022/v18i630384
Clustering coefficient is one of the most useful indices in complex networks. However, graph theoretic properties of this metric have not been discussed much in the literature, especially in graphs resulting from some binary operations. In this paper we present some expressions f...
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Research Article10.9734/arjom/2022/v18i630382
Harmonic centrality calculates the importance of a node in a network by adding the inverse of the geodesic distances of this node to all the other nodes. Harmonic centralization, on the other hand, is the graph-level centrality score based on the node-level harmonic centrality. I...
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Research Article10.9734/arjom/2022/v18i530377
For a nontrivial connected graph \(G\) with no isolated vertex, a nonempty subset \(D \subseteq V(G)\) is a rings dominating set if each vertex \(v \in V-D\) is adjacent to at least two vertices in \(V-D\). Thus, the dominating set \(D\) of \(V(G)\) is a rings dominating set if f...
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Research Article10.9734/arjom/2022/v18i12622