Researches Of Some Topology Indices In Graph Theory

In this dissertation, we mainly develop some results of topology indices, suchas Randi′c index, Zagreb index, K-connectivity index, etc. and get some moregeneral results. The ?rst chapter introduces some basic knowledge of graph theoryand related topology indices. Chapter II to Chapter V are the main results of thedissertation. In chapter II we develop the K-connectivity index of an in?nite classof dendrimer nanostars from the result of the second-connectivity index of suchgraph. In chapter III we develop the upper bound of Zagreb indices when givenseveral maximum and minimum degrees from from the result of the upper boundof Zagreb indices when given the maximum, second maximum and the minimumdegrees. In chapter IV we develop the upper bound and the lower bound of Randi′cindex of a connected graph when the maximum degree is not greater than ? andthe minimum degree is not less thanδfrom the result of the upper bound and thelower bound of Randi′c index of an alkane graph(the connected graph which themaximum degree is not greater than 4). In chapter V we develop the upper boundand the lower bound of zeroth-order general Randi′c index of a connected graphwhen the maximum degree is not greater than ? and the minimum degree is notless thanδfrom the result of the upper bound and the lower bound of zeroth-order general Randi′c index of a morecular graph(the connected graph which themaximum degree is not greater than 4), and construct extremal graphs to attainthe upper and lower bound.