Abstract
It is well known that the spiro and the polyphenyl hexagonal chains are graphs of a class of unbranched multispiro molecules and polycyclic aromatic hydrocarbons. Let be the degree-Kirchhoff index and Gut(G) be the Gutman index of a connected graph G. In this paper, we first give the formulae for calculating the Gutman indices and the degree-Kirchhoff indices of spiro and polyphenyl hexagonal chains, respectively. Then, we describe a relationship between the Gutman (resp. degree-Kirchhoff) indices of a spiro hexagonal chain and its corresponding polyphenyl hexagonal chain, and obtain the extremal values and characterize the extremal graphs with respect to the Gutman (resp. degree-Kirchhoff) indices among all spiro and polyphenyl hexagonal chains with n hexagons, respectively. Finally, we determine the bounds for
of spiro and polyphenyl hexagonal chains, respectively.
Acknowledgments
The authors would like to thank editor and the anonymous referees for their valuable comments and helpful suggestions for the improvement of the manuscript.
Disclosure statement
No potential conflict of interest was reported by the author(s).