Double hexagonal chains with maximal Hosoya index and minimal Merrifield–Simmons index

摘要

It is well known that the two graph invariants, “the Hosoya index” and “the Merrifield–Simmons index” are important ones in structural chemistry. The extremal hexagonal chains with respect to the Hosoya index and Merrifield–Simmons index are determined by Gutman and Zhang (J. Math. Chem., 12 (1993) 197–210, 27 (2000) 319–329 and J. Sys. Sci. Math. Sci., 18 (4) (1998) 460–465). In this paper, we will consider a type of the pericondensed hexagonal system. The double hexagonal chains with maximal Hosoya index and minimal Merrifield Simmons index are determined.