Graph Theory: A Lost Component For Development in Nigeria

Abstract

Graph theory is one of the neglected branches of mathematics in Nigeria but with the most applications in other fields of research. This article shows the paucity, importance, and necessity of graph theory in the development of Nigeria. The adjacency matrix and dual graph of the Nigeria map were presented. The graph spectrum and energies (graph energy and Laplacian energy) of the dual graph were computed. Then the chromatic number, maximum degree, minimum spanning tree, graph radius, and diameter, the Eulerian circuit and Hamiltonian paths from the dual graph were obtained and discussed.

A Review on Quadrant Interlocking Factorization: WZ and WH Factorization

“…We know that a simple graph G = (V, E) is an ordered pair consisting of a set of vertices V = {v 1 , v 2 , ..., v n } and a set of undirected edges E = {e 1 , e 2 , ..., e n }, no loops nor multiple edges permitted [49,50]. A mixed graph G = (V, E, A) is an ordered triple consisting of a set of vertices V = v 1 , v 2 , ..., v n , a set of undirected edges E = {e 1 , e 2 , ..., e n }, and a set of directed arcs A [51].…”

Application of hourglass matrix in Goldreich-Goldwasser-Halevi encryption scheme

“…Babarinsa and Kamarulhaili [18] gave details on hourglass matrix and its factorization algorithm by restricting the computed entries of the factorization to be nonzero in comparison with an hourglass device. They also suggested its applications in mathematics, graph theory, statistics, and computer science, see [19][20][21][22][23][24]. An hourglass matrix is defined as a nonsingular matrix of order n (n ≥ 3) with nonzero entries from the ith to the (n − i + 1) element of the ith and (n − i + 1) row of the matrix, 0's otherwise for i = 1, 2, ..., n+1 2 [18].…”

Examination Timetable Scheduling Using Graph Coloring for Faculty of Science

“…Graphs are classified into directed and undirected, weighted and unweighted, cyclic and acyclic. The adjacency matrix can used to draw the graph with several applications and different adjacency matrices exist such as mixed hourglass adjacency matrix, see (Babarinsa, 2022;Bashir, 2023).…”

“…Mathematically, a simple graph 𝐺 = (𝑉, 𝐸) consist of a set of vertices V and a set of undirected edges E (Bickle, 2020). A directed graph (or digraph) is a graph that contains only set of directed edges with the set of vertices V. A mixed graph 𝐺 = (𝑉, 𝐸, 𝐴) is an ordered triple consisting of a set of vertices 𝑉 = {𝑣 1 , 𝑣 2 , … , 𝑣 𝑛 } a set of undirected edges 𝐸 = {𝑒 1 , 𝑒 2 , … , 𝑒 𝑛 } and a set of directed edges (Rosen, 2012;Babarinsa, 2022). A weighted graph or a network is a graph in which a number (the weight) is assigned to each edge, weights represents things like costs, lengths or capacities, courses and many more depending on the problem at hand (Prathik, 2016).…”