The minimal and maximal energies of all cubic circulant graphs

Abstract

In recent article, Zhou and Zhou conjectured that among cubic circulant graphs with n vertices the maximum energy occurs whenever the largest number of components is attained. In this article, first we compute the upper and lower bounds for the energies of the isomorphic copies of Möbius ladder graph and the prism graph on n vertices then we explicitly determine the minimal and maximal energies of all cubic circulant graphs on n vertices.

Keywords

• maximal energy
• minimal energy
• trivalent graphs
• cubic graphs
• 3-circulant graphs
• möbius ladder graph
• prism graph
• taylor expansion