ON THE ANALYSIS OF SOME THEORETIC GRAPH PROPERTIES OF THE INTERSECTION GRAPH OF Zn
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Abstract
Abstract. This study investigates the structural properties of the Intersection Graph Γint(Zn) of the
subgroups of Zn, focusing on cases where n = p, n = pq, n = p2 (p, q primes), and n = 2k (k a natural
number). The research examines the connectedness of the graph. The results reveal unique properties of
Γint(Zn) for each case of connectedness. Notably, for n = 2k, the graph is regular, complete, and exhibits
rapid growth in size as k increases. This study provides a comprehensive understanding of the structural
properties of Γint(Zn) and contributes to the existing body of knowledge on graph theory and group theory.
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