Abstract
The variants of first Karnatak College Dharwad energy, in brief, the first [Formula: see text] energy, namely the first [Formula: see text] hyperenergeticity, the first [Formula: see text] borderenergeticity and the first [Formula: see text] equienergeticity, are defined. These concepts are further studied for complement, line graph and splitting graph of a graph. Lastly, some results on first [Formula: see text] equienergetic graphs are obtained.
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