Mixed Energy of a Mixed Hourglass Graph - Babarinsa, Olayiwola; Kamarulhaili, Hailiza (Communications in Mathematics and Applications, 2019)
In this paper we discuss a complete mixed graph called mixed hourglass graph. The direct representation of hourglass matrix in graph gives a weighted mixed hourglass graph. Then, we obtain a mixed hourglass graph from the weighted mixed hourglass graph by assigning its edge-labelled a numerical value of weight 1. Next, we derive the determinant, spectrum and mixed energy of the graph to conclude that the energy of a mixed hourglass graph coincides with twice the number of edges in the graph and the sum of the square of its eigenvalues.