Let　G　be　a　simple　graph　with　n　vertices　and　m　edges.　In　this　paper,　we　present　some　new　upper　bounds　for　the　adjacency　and　the　signless　Laplacian　spectral　radius　of　graphs　in　which　every　pair　of　adjacent　vertices　has　at　least　one　common　adjacent　vertex.　Our　results　improve　some　known　upper　bounds.　The　main　tool　we　use　here　is　the　Lagrange　identity.　©　2019,　Editorial　Committee　of　Applied　Mathematics.