University of KashanMathematics Interdisciplinary Research2538-36394220191201k-Intersection Graph of a Finite Set30531710261310.22052/mir.2020.208185.1178ENFahimeh EsmaeeliDepartment of Pure Mathematics,
Ferdowsi University of Mashhad,
Mashhad, I. R. IranAhmad ErfanianDepartment of Pure Mathematics and The Center of Excellence in Analysis on
Algebraic Structures,
Ferdowsi University of Mashhad,
Mashhad, I. R. Iran0000-0002-9637-1417Farzaneh MansooriDepartment of Pure Mathematics,
Ferdowsi University of Mashhad, International Campus
Mashhad, I. R. IranJournal Article20191109For 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.https://mir.kashanu.ac.ir/article_102613_b205b739f72772023b0d554c0ed5cdc2.pdf