Abstract
The sum of absolute values of eigenvalues of a graph G is defined as energy of graph. If the energies of two non-isomorphic graphs are same then they are called equienergetic. The energy of complete graph with n vertices is 2(n − 1) and the graphs whose energy is equal to 2(n − 1) are called borderenergetic graphs. It has been revealed that the graphs upto 12 vertices are borderenergetic. It is very challenging and interesting as well to search for borderenergetic graphs with more than 14 vertices. The present work is leap ahead in this direction as we have found a family of borderenergetic graphs of arbitrarily large order. We have also obtained three pairs of equienergetic graphs.
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