ON GRAPH ENERGY, MAXIMUM DEGREE AND VERTEX COVER NUMBER.

For a simple graph G with n vertices and m edges having adjacency eigenvalues λ₁;λ₂,...,λ_n, the energy E (G) of G is defined as E (G) = Σⁿ_i=1 |λ_i|. We obtain the upper bounds for E (G) in terms of the vertex covering number t, the number of edges m, maximum vertex degree d₁ and second maximum vertex degree d₂ of the connected graph G. These upper bounds improve some recently known upper bounds for E (G). Further, these upper bounds for E (G) imply a natural extension to other energies like distance energy and Randic energy associated to a connected graph G. [ABSTRACT FROM AUTHOR]