Scholarly work in the Department of Mathematics & Statistics

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Browsing Scholarly work in the Department of Mathematics & Statistics by Author "Ogundipe Opeoluwa Lawrence"

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    Hamiltonian Complete Number of Some Variants of Caterpillar Graphs
    (arXiv preprint, 2022) Adefokun Tayo Charles; Ajayi Deborah Olayide; Ogundipe Opeoluwa Lawrence; Onaiwu Kingsley Nosa
    A graph G is said to be Hamiltonian if it contains a spanning cycle. In this work, we investigate the Hamiltonian completeness of certain classes of caterpillar graphs, which are trees with a central path to which all other vertices are adjacent. For a non-Hamiltonian graph G, the Hamiltonian complete number H(G) is the minimum number of edges that must be added to G to make it Hamiltonian. We focus on both regular and irregular caterpillar graphs, deriving explicit formulas for H(G) in various cases. Specifically, we show that for a regular caterpillar graph Gn(k) where each vertex on the central path is adjacent to k leaves, H(Gn(k)) = n(k−1). We also explore irregular caterpillar graphs, where the number of leaves adjacent to each vertex on the central path varies, and provide bounds for H(G) in these cases. Our results contribute to the understanding of Hamiltonian properties in tree-like structures and have potential applications in network design and optimization.
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    On Induced Matching Numbers of Stacked-Book Graphs
    (International Journal of Mathematical Sciences and Optimization: Theory and Applications, 2024) Adefokun Tayo Charles; Ogundipe Opeoluwa Lawrence; Ajayi Deborah Olayide
    For a simple undirected graph G, an induced matching in G is a set of edges M no two of which have common vertex or are joined by an edge of G in the edge set E(G) of G. Denoted by im(G), the maximum cardinal number of M is known as the induced matching number of G. In this work, we probe im(G) where G = Gm,n, which is the stacked-book graph obtained by the Cartesian product of the star graph Sm and path Pn.