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Image of Discontinuity, Nonlinearity and Complexity
ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Eigenvalues and Energy from Minimum Edge Dominating Matrix in Caterpillars

Discontinuity, Nonlinearity, and Complexity 13(4) (2024) 593--600 | DOI:10.5890/DNC.2024.12.001

Fateme Movahedi

Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran

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Abstract

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.

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