Bounds on the Minimum Edge Dominating Energy in Terms of Some Parameters of a Graph

Abstract

‎The minimum edge dominating energy‎, ‎denoted by $EE_{F}(G)$‎, ‎is the sum of the absolute values of eigenvalues of the minimum edge dominating matrix of graph $G$‎. ‎In this paper‎, ‎we give some bounds and sharp bounds of $EE_{F}(G)$ in terms of matching number‎, ‎the number of positive eigenvalues of the minimum edge dominating matrix‎, ‎and the rank of $G$‎.

Keywords

• minimum edge dominating energy
• eigenvalue
• matching number
• rank