The Extremal Values of Topological Index of Caterpillars with Given Degree Sequence 

Author  LiuYong 
Tutor  ZhangXiaoDong 
School  Shanghai Jiaotong University 
Course  Applied Mathematics 
Keywords  topological index caterpillar Randi? index Wiener index 
CLC  O157.5 
Type  Master's thesis 
Year  2011 
Downloads  26 
Quotes  0 
Rand_{i}（?） ind_{e}x and_{ }Wiener ind_{e}x are two important molecular topological ind_{i}ces in chemical graph theory. Moreover, in the general research about graph theory, they also have important theoretical significances. So in this paper we will stud_{y} the two ind_{i}ces. In the paper, we will d_{i}scuss some properties of the extremal caterpillars which respectively attain the extremal values of Rand_{i}（?） ind_{e}x and_{ }Wiener ind_{e}x among all caterpillars with given d_{e}gree sequence. And_{ }accord_{i}ng to the properties, the structure of the extremal caterpillars will become clear.Firstly, we will use the method_{s} in algebra and_{ }graph theory to characterize the extremal caterpillar with the maximum/minimum Rand_{i}（?） ind_{e}x among all caterpillars with given d_{e}gree sequenceπ=（ d_{1} , d_{ }2, ..., d_{n}）, where d_{1} （?） d_{ }2 ?...（?） d_{ }k （?） 2（?） d_{k+1}=...=d_{n}=1 Moreover, subsequently we will learn that when k is fixed_{ }the extremal caterpillar with the maximum/minimum Rand_{i}（?） ind_{e}x is unique. In ad_{d}_{i}tion, we will point out the cond_{i}tion“d_{1} （?） d_{ }2 ?...?d_{k}”is ind_{i}spensable.Second_{l}y, we will consid_{e}r the Wiener ind_{e}x of the caterpillars with given d_{e}gree sequenceπ=（ d_{1} , d_{ }2, ..., d_{n}）, where d_{1} （?） d_{ }2 ?...（?） d_{ }k （?） 2（?） d_{k+1}=...=d_{n}=1 and_{ }characterize the extremal caterpillars which respectively attain the maximum and_{ }minimum Wiener ind_{e}x when k（?）6. And_{ }it should_{ }be noted_{ }that the result about the maximum Wiener ind_{e}x has been published_{ }in MATCH Commun. Math. Comput. Chem. 64（3）（2010）.At last, we will summarize the whole paper and_{ }propose several problems that need_{ }thinking in the future.