Ordering of minimal energies in unicyclic signed graphs

Tahir Shamsher, Mushtaq Bhat, Shariefuddin Pirzada*, Yilun Shang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
JournalRevista de la Union Matematica Argentina
DOIs
Publication statusAccepted/In press - 21 Sep 2021

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