Mixed Energy of a Mixed Hourglass Graph

Babarinsa, O; Kamarulhaili, H

Babarinsa, O (reprint author), Fed Univ Lokoja, Dept Math Sci, Lokoja 1154, Kogi State, Nigeria.

COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, 2019; 10 (1): 45

Abstract

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.

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