The Kirchhoff index and spanning trees of Möbius/cylinder octagonal chain

Abstract The Kirchhoff index and degree-Kirchhoff index have attracted extensive attentions due to their wide applications in physics and chemistry. These indices have been computed for many interesting graphs, such as linear polyomino chain, linear/Mobius/cylinder hexagonal chain, and linear octagonal chain. In the present paper, we consider Mobius octagonal chain ( M n ) and cylinder octagonal chain ( M n ′ ). Explicit closed-form formulae of the Kirchhoff index and the number of spanning trees are obtained for M n and M n ′ .