The general sum-connectivity index of a graph G is a molecular descriptor defined asdenotes the degree of vertex u in G and α is a real number. In this paper, we obtain the first third graphs with maximum general sum-connectivity index among the connected tricyclic graphs of order n for α ≥ 1 by four transformations which increase the general sum-connectivity index.

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The Wiener index of a connected k-uniform hypergraph is defined as the summation of distances between all pairs of vertices. We determine the unique k-uniform unicyclic hypergraphs with maximum and second maximum, minimum and second minimum Wiener indices, respectively.

Let H = (V, E) be a hypergraph and B its incidence matrix. Let Q(H) = BBT be the signless Laplacian matrix of H and λ1(Q), λ2(Q), …, λn(Q) are its eigenvalues. The signless Laplacian Estrada index of H is defined as italicSLEE()H=∑i=1neλi()Q which is first extended to hypergraph. We obtain lower and upper bounds for the index in terms of the number of vertices and edges of H. We also determine the unique graph with maximum SLEE among all k‐uniform hypergraphs. In addition, we characterize the extremal hypertrees with the smallest and the largest SLEE among all k‐uniform hypertrees.

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