TY - JOUR
T1 - Ordering of minimal energies in unicyclic signed graphs
AU - Shamsher, Tahir
AU - Bhat, Mushtaq
AU - Pirzada, Shariefuddin
AU - Shang, Yilun
N1 - The research of S. Pirzada is supported by the SERB-DST research project number MTR/2017/000084. The research of Tahir Shamsher is supported by SRF financial assistance by Council of Scientific and Industrial Research (CSIR), New Delhi, India.
PY - 2023/5/16
Y1 - 2023/5/16
N2 - 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.
AB - 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.
KW - Unicyclic signed graph
KW - spectrum
KW - energy
KW - ordering
U2 - 10.33044/revuma.2565
DO - 10.33044/revuma.2565
M3 - Article
VL - 65
SP - 119
EP - 133
JO - Revista de la Union Matematica Argentina
JF - Revista de la Union Matematica Argentina
SN - 0041-6932
IS - 1
ER -