… upper and lower bounds for E A α ( G ) in terms of graph parameters (the … bounds. We
also consider the relations between the α − adjacency energy and the other energies of a graph…

… S (G) is the energy and QE(G) is the signless Laplacian energy of G. In this paper, we obtain
… lower bounds for the generalized adjacency energy of a graph, in terms of different graph …

… of graphs, we find some lower bounds for the energy of graphs. … of G ‾ are adjacent if and
only if they are not adjacent in G. … of Theorem 2, we conclude that α 2 is an eigenvalue of G × G . …

… In this paper we are concerned with simple graphs, that is graphs without labeled,
directed, … Let G be such a graph of order n and size m, and let the eigenvalues of its (0, 1)-adjacency …

… 1 n | ρ i − 2 α m n | , where n is the order and m is the size of G. We obtain upper and lower
bounds for E A α ( G ) in … Further, we characterize the extremal graphs attaining these bounds. …

… of EAα (G) in terms of the order, the size and the first Zagreb index of G for α ∈ [1 … Gutman
[5] defined the energy of a graph G as the sum of absolute values of adjacency eigenvalues of …

… graph does not decrease its energy. Let G be a connected graph of order n and size m with
the adjacency matrix … Let x = α 2 n n 1 and y = β 2 n n 2 . Then the previous inequality can be …

… adjacency matrix weighted in a specific way. Using this new representation we find new
bounds for the energy … for any real α (here α = 1 2 ). Therefore we can write (11) | A | = λ 1 ∑ k = …

… m × n nonnegative matrix with maximum entry α, and A 1 ⩾ nα. … If A is the adjacency matrix
of a graph, this inequality is tight … lower bounds for the energy of “almost all” d-regular graphs. …

… can write the adjacency matrix of G as A ( G ) = [ 0 α 0 α T B X 0 X T C ] , where α is a row
vector with columns indexed by the vertices of N, and [ B X X T C ] is the adjacency matrix of H. …