TY  - BOOK
AU  - Estrada,Hannah I.
AU  - Navarro,Camille R.
AU  - Sopeña,John Earl M.
TI  - On properties of kp-restricted intersection graph / 
N1  - Undergraduate Thesis (BSAM)- Applied Mathematics; Includes bibliographical references
N2  - The graphs in this study involve the concepts of sets and intersections and are classified as simple and regular graphs. This study introduces a new class of the k-restricted intersection graphs and discusses its fundamental properties which includes order, size, vertex degree, and special cases. Let Sn be a set of n elements, and let S(n, k) be the collection of all k-element subsets of Sn. The kp-restricted intersection graph, denoted by G p S(n,k) , is defined on S(n,k) such that two vertices are adjacent whenever their intersection contains exactly p elements. Formulas for the order, size and vertex degree were derived. Special cases under specific values of n, k, and p are also presented. The study also determines the possible values of p for certain values of k. There are specific conditions of kp-restricted intersection graphs that guarantees the resulting graph is complete. Other special cases produce empty graph. Moreover, the union of a certain kp-restricted intersection graphs was shown to be isomorphic to a complete graph
ER  -