Bounds Of Graph Energy In Terms Of Domination Number

Let G be an undirected graph without loops and multiple edges.A dominating set of G is a subset of V（G）such that every vertex not in D is adjacent to at least one member of D.The domination number γ（G）of G is the number of vertices in a smallest dominating set of G.The energy ε（G）of G is the sum of the absolute values of all eigenvalues of G.In this paper,we are devoted to bound graph energy in terms of domination number.The paper is divided into four chapters.The first chapter introduces the research history and status,we also introduce some basic definitions and writing background related to our topic.In chapter 2,use some existing conclusions to prove that for a graph G without isolated vertices,thenε（G）≥2γ（G）,the equality holds if and only if every connected component of G is P2 or C4.In chapter 3,we devote to prove that for a graph G without isolated vertices,then ε（G）≤（△+1）(（△+1）^1/2+1)/2γ²（G） where △ is the maximun vertex degree of G,and the equality holds if and only if G = K4.