Brazal, Maricel O. creator author. Ortega, Louise Geil L. author. Salona, Denise Lynne D. author. Jagmis, Jiel Mark D., adviser. Magtibay, Francis Gerard C., chair, panelist. Nieva, Alex Ralph B., panelist. Torino, Jovanie G., panelist. text bibliography ph 2026 monographic eng

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59 leaves. This paper explores the j-edge intersection graph as applied specifically to the hairy cycle, denoted by EH(k,j) . Graph EH(k,j) is a graph whose vertex set consists of the spanning subgraphs of a hairy cycle Hk with j edges, where k ≥ 3 and j is a non- negative integer such that 1 ≤ j ≤ 2k. Two vertices are adjacent if their respective spanning subgraphs share exactly one common edge. Graph EH(k,j) is considered a simple graph, containing neither loops nor multiple edges. When j = 0 or j > 2k, the graph EH(k,j) cannot be constructed, whereas when j = 1, it produces an empty graph. It can also be a trivial graph if and only if j = 2k. Furthermore, this paper determines fundamental parameters of this graph, such as order, degree, and size, that can contribute to a deeper understanding of the j-edge intersection graph of hairy cycles and extend existing work in intersection graphs. Maricel O. Brazal, Louise Geil L. Ortega, and Denise Lynne D. Salona. Undergraduate Thesis (BSAM)- Applied Mathematics. Camarines Sur Polytechnic Colleges, 2026. Includes bibliographical references. CSPC 260804 20260804143545.0 eng