we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.

Sei Murakami, Dr. Eng. Haruo Suzuki Keisuke Shibuya, Dr. Sc. OVERVIEW: The development of innovative pharmaceuticals with potential for meeting unmet medical needs and vaccines that protect against infectious diseases is very important for ensuring people’s health and welfare. However, biopharmaceuticals and vaccines that make these developments possible are more easily affected by the producti...

The structure of phase space is determined for spatially compact and locally homogeneous universe models with fluid. Analysis covers models with all possible space topologies except for those covered by S, H or S × R which have no moduli freedom. We show that space topology significantly affects the number of dynamical degrees of freedom of the system. In particular, we give a detailed proof of...

The Merrifield-Simmons index is related to several physicochemical characteristics and is thus of use in combinatorial chemistry, e.g. in drug design and molecular recognitions. In this paper, we show how one can algorithmically construct databases of acyclic molecular graphs with large Merrifield-Simmons index. Our algorithm can deal with a large number of atoms (several hundreds) in short tim...