On The Nullity Of Three Types Polygonal Chain Graphs

The nullity is the number of zero eigenvalues in the spectrum of the graph G, and isdenoted byη(G). Nullity is one of the invariants of the graph spectra, and is the basis inves-tigating problems of graph spectra theory. About which we have many important conclu-sions, we can see these papers [5-19,24,37]. The graph spectra theory have many importantbackground applications in a number of subjects, especially in chemistry subject. The nul-lity of the chemical molecular structure graph, which re?ect the stability of the chemicalmolecular structure graph.This paper studys the nullity of the cactus chain graph , polygonal joint chains graph,and polygonal bridge ring chains graph by according the conclusion that has been studyed.So we learn the stability problem of the chemical molecular graph by their nullity.The nullity of these three types polygonal chain graphs , which are discussed in thesecond chapter, the third chapter and the fourth chapter of this thesis. Firstly, we get theconcepts of three types polygonal chain graphs by constructing graphs respectively. Thenwe use the relation between the graph and its induced subgraph, and we can get the relationbetween their nullity. So as that we can get the nullity of former graph.In the first part, we introduce the domestic and foreign researching situations, and thegeneral knowledge.In the second chapter of this thesis, we investigate the problem on nullity of the cactuschain graph.At first we investigate the nullity of the general cactus chain graph, and then weobtain the nullity of the special chain hexagonal cactus. At last we obtain the nullity of thecactus chain graph whose every polygonal is odd circle.In the third chapter of this thesis, we investigate the problem on nullity of the polygonaljoint chains graph.At first we investigate the nullity of the general polygonal joint chains,and then we obtain the nullity of the poly phenyl chain.In the fourth chapter of this thesis, we study the problem on the nullity of the polygonalbridge ring chains graph. At first we investigate the nullity of the general polygonal bridgering chains graph, and then we obtain the nullity of the hexagonal chains.