The Influence Of The Change Of The Edge On The Two Types Of Energy Of The Graph

Graph energy comes from theoretical chemistry,which is an important branch of graph theory,and has a wide range of application value.In recent decades,many scholars have made extensive research on graph energy with the help of matrix method.In this paper,we mainly study the change of distance energy and Seidel energy of Complete Multipartite Graphs when one edge is deletedThe main content of this paper consists of two partsIn the first part:It is proved that for complete r-graph Kp,p,...,p with p>2,as well as the tripartite Turan graph T(n,3)with n≥ 6,the distance energy is always increased when an edge is deleted.The conjecture in[14]that the distance energy of a complete multipartite graph is increased by deleting edges is partly solved.Subsequently,it is proved that,for any positive integer r,there exists a class of graphs that have r positive eigenvalues,but the distance energy of these graphs is always increased when an edge is deletedIn the second part:The influence of edge deletion on the Seidel energy of complete tripartite graphs is mainly studied.In particular,tripartite Turan graph T(n,3)is a special complete tripartite graph.It is proved that for tripartite Turan graph T(n,3)with n≥9,the Seidel energy is always increased when an edge is deleted.