Some Upper Bounds for the Net Laplacian Index of a Signed Graph

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