Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2026 01 31 A note on the Estrada index of signed graphs 15094 10.22049/cco.2026.31379.2838 EN Subarsha Banerjee JIS University Journal Article 2025 12 29 The Estrada index is a spectral invariant with wide applications in graph theory and network science, and has been studied for both unsigned and signed graphs. In this paper, we investigate its extremal behavior over all signatures of a fixed<br />underlying graph. We prove that for any connected graph balanced signatures are the only ones that maximize the Estrada index. Signed graph Estrada index spectral moment balanced signature antibalanced signature https://comb-opt.azaruniv.ac.ir/article_15094_1f3fbe804015bc108bac9ef4ceb2237f.pdf