For any graphs G of order n, the spanning tree packing number, denoted by, of a graph G is the maximum number of edge disjoint spanning tree contained in G. In this study determine the spanning packing number of lexicographic product of graphs resulting from two path graphs.
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Research Article10.9734/arjom/2023/v19i9710
For any graph G, the spanning tree packing number of \(\sigma\) (G), is the maximum number of edge-disjoint spanning trees contained in G. In this study, we determined the maximum number of edge-disjoint spanning trees of the generalized petersen graph and cocktail graph.
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Research Article10.9734/arjom/2023/v19i9714
For a nontrivial connected graph G, a non-empty set S \(\subseteq\) V (G) is a bipartite dominating set of graph G, if the subgraph G[S] induced by S is bipartite and for every vertex not in S is dominated by any vertex in S. The bipartite domination number denoted by \(\gamma\)b...
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Research Article10.9734/arjom/2023/v19i5658
For a nontrivial connected graph G with no isolated vertex, a nonempty subset D \(\subseteq\) V (G) is a rings dominating set if D is a dominating set and for each vertex \(\upsilon\) \(\in\) V \ D is adjacent to at least two vertices in V \ D. Thus, the dominating set D of V (G)...
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Research Article10.9734/arjom/2023/v19i4649
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
A set S of a graph G = (V (G);E(G)) is a rings dominating set if S is a dominating set and for every vertex in the complement of S has atleast two adjacent vertices. The caridinality of the minimum rings dominating set is the rings domination number of graph G, denoted by \(\gamm...
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Research Article10.9734/arjom/2022/v18i12621
set S of vertices in a graph G = (V (G);E(G)) is a hinge dominating set if every vertex \(u\) \(\in\) V \(\setminus \) \(S\) is adjacent to some vertex \(u\) \(\in\) \(S\) and a vertex \(w\) \(\in\) V \(\setminus\) \(S\) such that (\(v\), \(w\)) is not an edge in E(G). The hinge...
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Research Article10.9734/arjom/2022/v18i930404
For a connected simple graph G , a non-empty set \(S \subseteq V(G)\) of vertices is a safe set if, for every component \(A \text { of }\langle S\rangle_{G}\) and every component \(B \text { of }\langle V(G)-S\rangle_{G}\) adjacent to A , it holds that \(|A| \geq|B|\). The safe...
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Research Article10.9734/arjom/2022/v18i930399
Let G be a nontrivial, undirected, simple graph. Let S be a subset of V (G). S is a restrained cost effective set of G if for each vertex v in S, degS(v) \(\leq\) degV (G)rS(v) and the subgraph induced by the vertex set, V (G) r S has no isolated vertex. The maximum cardinality o...
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Research Article10.9734/arjom/2022/v18i830395