A Note on Biregular and Triregular hyperenergetic graphs

Résumé

If G is a molecular graph with eigenvalues μ1, μ2, μ3, ..., μp for the
adjacency matrix of G then, energy ζ(G) of graph G is the sum of the absolute
values of μi’s. The graphs having energy greater than the energy
of complete graph are known as hyperenergetic graphs. Mathematically
we say G is hyperenergetic if it satisfies the equation ζ(G) > (2p − 2),
where p is the count of vertices in G. In [1], [8], [6] the authors have studied
various hyperenergetic graphs and established many results regarding
hyperenergetic graphs. In this research paper we obtain constraints
for a graph to be hyperenergetic which are biregular and triregular in
terms of count of their vertices and edges.