We present explicit formula for the general Randić connectivity, general sum-connectivity, Hyper-Zagreb and Harmonic Indices, and Harmonic polynomial of some simple connected molecular graphs.

Recently Prof.Chandrashekar Adiga et al. [1] have defined the minimum covering energy, E C (G) of a graph G which depends on its particular minimum cover C. Motivated by this paper, we introduced the concept of minimum covering distance energy E Cd (G) of a graph G and computed minimum covering distance energies of a star graph, complete graph, crown graph, bipartite graph and cocktail graphs. Upper and lower bounds for E Cd (G) are also established. Mathematics Subject Classification: 05C50, 05C69

In this paper we computed minimum covering Harary energies of a star graph, complete graph, crown graph, bipartite graph and cocktail party graphs. Upper and lower bounds for minimum covering Harary energies are also established.

Let G be a graph with n vertices and m edges. The term energy of a graph G was introduced by I. Gutman in chemistry due to its relevance to the total π-electron energy of a carbon compound. An analogous energy , called the distance energy, was defined by Indulal et al. (MATCH Commun. Math. Comput. Chem. 60:461–472, 2008) in 2008. McClelland and Koolen–Moulton bounds for distance energy were established subsequently by Ramane et al. (Kragujev. J. Math. 31:59–68, 2008). The lower and upper bounds for obtained in this paper are better than the McClelland and Koolen–Moulton bounds.

In organic chemistry, finding out theoretically the total π−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, 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 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.