The j-edge intersection graph of hairy cycle / Maricel O. Brazal, Louise Geil L. Ortega, and Denise Lynne D. Salona.

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Dissertation note: Undergraduate Thesis (BSAM)- Applied Mathematics. Camarines Sur Polytechnic Colleges, 2026. Abstract: 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.
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Unpublished Materials Unpublished Materials Main Library Undergraduate Thesis Section UTH BSAM B827j 2026 (Browse shelf(Opens below)) 1-1 Not for loan 007404UM

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

Includes bibliographical references.

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.

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