The energy of a graph G, denoted by E(G), is defined to be the sum of absolute values of all eigenvalues of G. Let \(\fancyscript{U}_{n}\) denote the set of connected (n, n)− graphs, i.e., the connected graphs with n vertices and n edges. For any graph \(G\in\fancyscript{U}_{n}\) , if \(d(v) = r(\geq 2)\) for each vertex v in the unique cycle of G, G is said to be cycle−r−regular (n, n)− graph. In this paper, cycle−3−regular (n, n)− graph with minimal energy is uniquely determined.
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Wang, M., Hua, H. & Wang, D. Minimal energy on a class of graphs. J Math Chem 43, 1389–1402 (2008). https://doi.org/10.1007/s10910-007-9259-1
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DOI: https://doi.org/10.1007/s10910-007-9259-1