8477

7858

كارشناسي ارشد

رياضي محض﴿جبر﴾

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1392

[شش] ، 91ص.: مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

بيژن طائري

منصور آقاسي

8/11/92

قهرمان طاهريان، اعظم اعتماد

رياضي

ID7858

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Abstract This Msc thesis is based on the following paper Devos M Goddyn L Mohar B Samal R Cayley sum graphs and eigenvalues of fullerenes Journals of Combinatorial Theory Series B over Let Let G be a group and S be an arbitrary subset of G The Cayley sum graph with respect labeled as The adjacency matrix of matrix with entery equals to to is a graph with vertex set V G and edge set be a graph with vertices is an are eigenvalues of together with their multiplicities We shall usually refer to the eigenvalues of if vertices and are adjacent and otherwise The spectrum of a graph is the set of numbers which as the eigenvalues of The aim of this thesis is to determine the spectrum of cubic plane graphs whose faces have size and their eigenvalues come in pairs of the form A semiedge of a graph is an edge with one endpoint Such graphs called fullerenes In particular we study a conjecture of Fowler which asserts that all but unlike a loop A fullerenes is a connected regular graph possibly with semiedges embedded in the plane and mentions semiedges as faces of length We study the extension of where one of the following holds conjecture of Fowler et al as follow if G is a fullerene with s semiedges then the spectrum of G may be partitioned as A s and or B s and C s and D s and Then we see that each fullerene is isomorphic to a cayley sum graph for an abelian group which can be generated by two elements We study an algorithm utilizes a geometric representation to recognize the algebraic structure of these graphs which turn out to be examples of cayley sum graphs This algorithm helps us to study about these fullerenes more precisely Then by using linear algebra we can exactly determine which cayley sum graphs are isomorphic to a certain fullerene In this way group and subset of cayley sum graph will recognize and by use of theorems which are about the spectrum of these graphs spectrum of fullerenes are computed PDF created with pdfFactory trial version www pdffactory com

بيژن طائري

منصور آقاسي

قهرمان طاهريان، اعظم اعتماد