ENERGY OF GRAPHS AND ITS NEW BOUNDS

Abstract

In organic chemistry, finding out theoretically the total $\pi-$electron energy of conjugated carbon compound is one of the interesting concept. Later during the year 1970, I. Gutman was successful in achieving this by defining a term called energy of a graph, $\mathbb{E}(G)$ for any graph $G$ with $m$ edges and $n$ vertices. It is not that easy to find energy of any general graph. This problem was solved by obtaining bounds for $\mathbb{E}(G)$. Initially bounds for energy of any graph $G$ are obtained by using McClelland bounds. Koolen and Moulton improved the McClelland's upper bounds. In this article we established new energy bounds with the help of Holder's inequality.