k-Intersection Graph of a Finite Set

Document Type: Original Scientific Paper

Authors

1 Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, I. R. Iran

2 Department of Pure Mathematics and The Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, Mashhad, I. R. Iran

3 Department of Pure Mathematics, Ferdowsi University of Mashhad, International Campus Mashhad, I. R. Iran

10.22052/mir.2020.208185.1178

Abstract

For any nonempty set Ω and k-subset Λ, the k-intersection graph, denoted by Γm(Ω,Λ), is an undirected simple graph whose vertices are all m-subsets of Ω and two distinct vertices A and B are adjacent if and only if A∩B ⊈ Λ. In this paper, we determine diameter, girth, some numerical invariants and planarity, Hamiltonian and perfect matching of these graphs. finally we investigate their adjacency matrices.

Keywords


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Volume 4, Issue 2
Special Issue: Spectral Graph Theory and Mathematical Chemistry with Connection to Computer Science
Autumn 2019
Pages 305-317