On the atom-bond sum-connectivity spectral radius of unicyclic graphs

Let G be a graph with n vertices.For i = 1, 2, . . ., n, let di be the degree of vertex vi in G.The atom-bond sum-connectivity (ABS) matrix of G is an n n matrix whose (i, j)-entry is equal to (di + dj -2)/(di + dj) if the vertices vi and vj are adjacent, and 0 otherwise.The ABS spectral radius of G, denoted by 1(G), is the largest eigenvalue of the ABS matrix of G. Let Cn be the cycle graph with n vertices.Let U 1 n be the unicyclic graph with n vertices and maximum degree n -1.For a unicyclic graph G with n 17 vertices, we prove that 1(Cn) 1(G) 1(U 1 n ), where the left equality holds if and only if G = Cn and the right equality holds if and only if G = U 1 n .