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If G is a molecular graph with n vertices and if ?1, ?2, ..., ?n are its eigenvalues, then the energy of G is equal to E(G) = |?1| + |?2|+ ... + |?n|. If E(G) > 2n - 2, then G is said to be hyperenergetic. We show that no H?ckel graph (= the graph representation of a conjugated hydrocarbon within the H?ckel molecular orbital model) is hyperenergetic.

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Energy of a graph is an interesting parameter related to total π electron energy of the corresponding molecule. Recently Vaidya and Popat defined a pair of new graphs and obtained their energy in terms of the energy of original graph. In this paper we generalize the construction and obtain their energy. Also we discuss the spectrum of the first level thorn graph of a graph.

Abstract.A dendroid is a connected semigraph without a strong cycle. In this paper, we obtain the various results on the enumeration of the non-isomorphic dendroids containing two edges and the dendroids with three edges.