Some New Bounds for α-Adjacency Energy of Graphs

Let G be a graph with the adjacency matrix A(G), and let D(G) diagonal of degrees G. Nikiforov first defined Aα(G) as Aα(G)=αD(G)+(1−α)A(G), 0≤α≤1, which shed new light on A(G) Q(G)=D(G)+A(G), yielded some surprises. The α−adjacency energy EAα(G) is invariant that calculated from eigenvalues Aα(G). In this work, by combining theory structure properties, we provide upper lower bounds for in terms parameters (the order n, edge size m, etc.) characterize corresponding extremal graphs. addition, obtain relations between other energies such E(G). Some results can applied to appropriately estimate α-adjacency using given rather than performing tedious calculations.