The intersection graph of isomorphic subgraphs of a graph

Authors

Mark Anthony A. Garcia, De La Salle University, Manila
Severino V. Gervacio, De La Salle University, Manila
Michelle G. Tan, De La Salle University, Manila

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Conference Proceeding

Source Title

Proceedings of the Eleventh OU-DLSU Academic Research Workshop

Volume

11

First Page

73

Last Page

75

Publication Date

2008

Abstract

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; P_m) is a complete graph for some conditions and show that Ω(G; H) is regular for some conditions.

html

Recommended Citation

Garcia, M. A., Gervacio, S. V., & Tan, M. G. (2008). The intersection graph of isomorphic subgraphs of a graph. Proceedings of the Eleventh OU-DLSU Academic Research Workshop, 11, 73-75. Retrieved from https://animorepository.dlsu.edu.ph/faculty_research/6075

Disciplines

Mathematics

Keywords

Intersection graph theory; Isomorphisms (Mathematics)

Upload File

wf_no