The intersection graph of isomorphic subgraphs of a graph
The intersection graph of a collection C of subsets of an arbitrary set X is the graph whose vertex-set is C where distinct vertices A, B ∈ C are adjacent if and only if A ∩ B ≠ ø. Let G and H be graphs and let G(H) be the collection of all subgraphs of G isomorphic to H. The graph with vertex-set G...
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| Main Authors: | , , |
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| Format: | text |
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Animo Repository
2008
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/faculty_research/6075 |
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| Institution: | De La Salle University |
| Summary: | The intersection graph of a collection C of subsets of an arbitrary set X is the graph whose vertex-set is C where distinct vertices A, B ∈ C are adjacent if and only if A ∩ B ≠ ø. Let G and H be graphs and let G(H) be the collection of all subgraphs of G isomorphic to H. The graph with vertex-set G(H) where to distinct vertices (subgraphs of G) A, B ∈ G(H) are adjacent if and only if V(A)∩V(B) ≠ ø is called intersection graph of subgraphs of G isomorphic to H and is denoted by Ω(G; H). We state and prove theorems regarding orders of Ω(G; P3) and Ω(G; P4). We also prove that Ω(G; Pm) is a complete graph for some conditions and show that Ω(G; H) is regular for some conditions. |
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