On the minimum energy of regular graphs

New Spectral Results for Laplacian Harary Matrix and the Harary Laplacian-Energy-like Applying a Matrix Order Reduction

“…From Theorem 9, we have that 2n−a 2 is an eigenvalue of RL(GW a,n−a ) with multiplicity a − 1. From Corollary 3, we have that the largest and smallest eigenvalues of RL(G) are the largest and smallest eigenvalues of F a+1 matrix given in (5). Then, we obtain the spectral radius applying the fact that the trace of the matrix is equal to the sum of its eigenvalues.…”

“…It should be noted that the interest for this graph invariant goes far beyond chemistry; for example, it is used for minimum and maximum energy for certain families of graphs [5][6][7], on upper and lower bounds for the energy of graphs [8][9][10][11], and the extension of energy to the Laplacian energy of graphs [12]. Additionally, in [13], the authors list various papers published in 2019 on graph energies, and summarize their main collective characteristics, but an interesting motivation is that the authors cite articles that show applications of graph energy outside the field of mathematics.…”

Some Less Familiar Properties of Randić Index

“…In contrast to this, graph energy of regular graphs has a pronounced sensitivity to their structure. [28,59,60]…”

Energy of a graph and Randic index

“…Other interesting old and new inequalities for the energy of a graph are derived. These inequalities relate the energy with different combinatorial quantities, such as the matching number [16], Hamiltonian paths and cycles [8], and {1, 2}-factors [1].…”