Let G be a graph. We say that hypergraph H is Berge-G if there bijection ?:E(G)?E(H) such e??(e) for all e?E(G). For any r-uniform and real number p?1, the p-spectral radius ?(p)(H) of defined as?(p)(H):=maxx?Rn,?x?p=1?r?{i1,i2,…,ir}?E(H)xi1xi2?xir. In this paper, we study hypergraphs. determine 3-uniform hypergraphs with maximum p?1 among when path, cycle or star.

A wheel graph is a formed by connecting single vertex to all vertices of cycle. called wheel-free if it does not contain any as subgraph. In 2010, Nikiforov proposed Brualdi–Solheid–Turán type problem: what the maximum spectral radius order n that subgraphs particular kind. this paper, we study problem for graphs, and determine (signless Laplacian) n. Furthermore, characterize extremal graphs.

Introduction/purpose: Vertex-degree-based (VDB) graph matrices form a special class of matrices, corresponding to the currently much investigated vertex-degree-based invariants. Some spectral properties these are investigated. Results: Generally valid sharp lower and upper bounds established for radius any VDB matrix. The equality cases characterized. Several earlier published results shown be ...

Rigidity is the property of a structure that does not flex under an applied force. In past several decades, rigidity graphs has been widely studied in discrete geometry and combinatorics. Laman (1970) obtained combinatorial characterization rigid $\mathbb{R}^2$. Lovász Yemini (1982) proved every $6$-connected graph Jackson Jordán (2005) strengthened this result, showed globally Thus with algebr...