| The energy of a graph G = (V,E) is defined as the sum of the absolute values its all eigenvalues.That is:E(G) = Yh=i I -^ I- This paper which stands on the basis of previous results,and which further research on the issue of the energy of some Bipartite graph,mainly includes:In chapter l,We introduce some basic terminology and notations,the research background and profound discussion on the status quoof Graph nenrgy ,and shows the main result's of this paper.In chapter 2,We main talk about (n, rn)—Bipartite graph and we obtain the second to fourth small graph.A caterpillar is a tree in which a removal of all pendant vertices makes a path .let T (n,d;ni,ri2, ...n^-i) G Tn/i be a caterpillar obtained from a path vq,v\, ...vri by attaching ni(ni > 0) pendant edges to Vi, (i = 1, 2,..., d—1).clearly,n = d + 1 + X^=i ni\In chapter 3,we main talk about the trees with a given diameter between 3and5 and obtain the second to fourth small graph.when d = 3,T(n, 3; 1, n—5) is the only second small graph;T(n, 3; 3, n—6) is the only third small graph;T(n, 3; 3, n—7) is the only fourth small graph;when d = 4,T(n,4; 1, 0, n—6) is the only second small graph;T(n, 4; 0, n—5,0) is the only third small graph;T(n, 4; 2,0, n—7) is the only fourth small graph;when d = 5,T(n, 5; 0, n—6,0, 0) is the only second small graph;T(n, 5; 1,0, 0, n—7) is the only third small graph;T(n, 5; 2, 0,0, n—8) is the only fourth small graph;In chapter 4,we propse some problems for farther reasure Bipartite graph. |
