LAUSR

The net Laplacian matrix $$N_{\dot{G}}$$ N G ˙ of a signed graph $$\dot{G}$$ G ˙ is defined as $$N_{\dot{G}}=D_{\dot{G}}^{\pm }-A_{\dot{G}}$$ N G ˙ = D G ˙ ± - A G ˙ , where $$D_{\dot{G}}^{\pm }$$ D G ˙ ± and $$A_{\dot{G}}$$ A G ˙ denote the diagonal matrix of net-degrees and the adjacency matrix of $$\dot{G}$$ G ˙ , respectively. In this study, we give two upper bounds for the largest eigenvalue of $$N_{\dot{G}}$$ N G ˙ , both expressed in terms related to vertex degrees. We also discuss their quality, provide certain comparisons and consider some particular cases.