The intersection graph of isomorphic subgraphs of a graph

• Main Authors: Garcia, Mark Anthony A., Gervacio, Severino V., Tan, Michelle G.
• Format: text
• Published: Animo Repository 2008
• Subjects: Intersection graph theory; Isomorphisms (Mathematics); Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/faculty_research/6075
• Institution: De La Salle University

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.