Eigenvalues and Energy from Minimum Edge Dominating Matrix in Caterpillars - Movahedi, Fateme (Discontinuity, Nonlinearity, and Complexity, 2026)
A caterpillar is a tree in which the removal of all pendant vertices makes it a path. Caterpillar trees have been used in chemical graph theory to represent the molecular structures of hydrocarbons. One of the important graph invariants based on a minimum edge dominating matrix of a graph is the minimum edge dominating energy of the graph. The minimum edge dominating energy of a graph G is defined as the sum of the absolute values of the eigenvalues of the minimum edge dominating matrix of G with respect to a minimum edge dominating set in G. In this paper, we obtain a minimum edge dominating set and the minimum edge domination number of caterpillar trees. Also, some results of the minimum edge dominating energy on caterpillars are given. We compute explicit formulas for the minimum edge dominating eigenvalues of these graphs.