Ordering of minimal energies in unicyclic signed graphs

Shamsher, Tahir, Bhat, Mushtaq, Pirzada, Shariefuddin and Shang, Yilun (2023) Ordering of minimal energies in unicyclic signed graphs. Revista de la Union Matematica Argentina, 65 (1). pp. 119-133. ISSN 0041-6932

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Abstract

Let S = (G, σ) be a signed graph of order n and size m and let t1, t2, . . . , tn be the eigenvalues of S. The energy of S is defined as E(S) = Pnj=1|tj|. A connected signed graph is said to be unicyclic if its order and size are same. In this paper, we characterize, up to switching, theunicyclic signed graphs with first 11 minimal energies for all n ≥ 12. For 3 ≤ n ≤ 7, we provide complete ordering of unicyclic signed graphs with respect to energy. For n = 8, 9, 10 and 11, we determine unicyclic signed graphs with first 13 minimal energies respectively.

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