The Spectral Characterization Of Graph With Odd Circuits

A graph G is said to be determined by its spectrum if for any graph H,φ(H,λ) =φ(G,λ) implies that H is isomorphic to G. In this paper, we give the parameterΠ, whichis related to some graph invariants. Some properties ofΠare given also . In those graphswithΠ= -1, we find a special graph with odd circuits. By the results, we show that thespecial graph with odd circuits is determined by its spectrum.In Chapters 1, we introduce some known results on spectral charaterization.In Chapters 2, we introduce basic notations and some lemmas, which prepare for-lowing two chapters.In Chapters 3, we give the definition and some properties of parameterΠand theirproof.In Chapters 4, first, we give the proof of three lemmas. By the results, we give theproof of main result.We conclude in Chapter 5 of the thesis by discussing some problems for furtherreseach.