(untitled)
The problem on intersection graph was introduced by Szpilrajn-Marczewski in 1945. This study introduces a new variant of intersection graph, called the k-restricted intersection graph. Let S_n be a nonempty n-element set, for some positive integer n and let S_(n,k) be the set of all the k-element subsets of S_n where 0≤ k≤ n. A k-restricted intersection graph, denoted by G_S_(n,k) , is a graph with vertex set S_(n,k) such that two vertices A,BS_(n,k) are adjacent whenever AB eq and A eq B. Here, we determined the order and size of G_S_(n,k) . Moreover, some parameters such as independence number, domination number, and isolate domination number of the k-restricted intersection graph were established. Finally, necessary and sufficient conditions for a G_S_(n,k) to be isomorphic to the cycle graph and complete graph were determined. , number=3, journal=European Journal of Pure and Applied Mathematics, year=2024, month=Jul., pages=1779–1803