On properties of kp-restricted intersection graph / Hannah I. Estrada, Camille R. Navarro, and John Earl M. Sopeña.

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Dissertation note: Undergraduate Thesis (BSAM)- Applied Mathematics. Camarines Sur Polytechnic Colleges, 2026. Abstract: 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.
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Unpublished Materials Unpublished Materials Main Library Undergraduate Thesis Section UTH BSAM E821o 2026 (Browse shelf(Opens below)) 1-1 Not for loan 007403UM

Undergraduate Thesis (BSAM)- Applied Mathematics. Camarines Sur Polytechnic Colleges, 2026.

Includes bibliographical references.

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.

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