### Comparing energy and Randic energy

#### Abstract

The recently conceived Randić energy (*RE*) is examined, and its relation to the (earlier much studied) total π-electron energy (*E*) is investigated. Within classes of molecular graphs, there exists a relatively good (increasing) linear correlation between *RE *and* E. *However, several significant differences between the structure-dependencies of *RE *and* E* have been discovered, the most striking of which is their dependence on the number *m* of edges of the underlying graph. Whereas, with increasing *m*, the average value of *E *increases, reaches a maximum and then decreases, the average value of *RE* monotonically decreases. The structure of the connected graph with a fixed number of vertices and maximal *RE* value was established.

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DOI: http://dx.doi.org/10.20450/mjcce.2013.127

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