### The Minimum Edge Covering Energy of a Graph

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**Authors:**S. SABETI, A. B. DEHKORDI AND S. M. SEMNANI

**DOI:**10.46793/KgJMat2106.969S

**Abstract:**

In this paper, we introduce a new kind of graph energy, the minimum edge covering energy, E

_{CE}(G). It depends both on the underlying graph G, and on its particular minimum edge covering C

_{E}. Upper and lower bounds for E

_{CE}(G) are established. The minimum edge covering energy and some of the coeﬃcients of the polynomial of well-known families of graphs like Star, Path and Cycle Graphs are computed.

**Keywords:**

Minimum edge covering set, minimum edge covering matrix, graph energy, minimum edge covering eigenvalues.

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