The Anti-adjacency Energy And Inertia Of Some Special Graphs

The anti-adjacency energy of graphs is derived from chemical graph theory,so it is meaningful to study its algebraic invariants.In this paper,we study the change of antiadjacency energy and inertia of complete r-partite graph before and after deleting edges,calculate the anti-adjacency energy and inertia of three kinds of special graphs,and obtain the maximum anti-adjacency energy of complete r-partite graph and the minimum anti-adjacency energy of three kinds of special graphs.In chapter 1,we introduce the research background of the anti-adjacency energy of graphs,the related concepts of graph theory and the research status of the anti-adjacency energy of some special graphs.In chapter 2,we first calculate the anti-adjacency energy and inertia of complete r-partite graph,then study the change of the anti-adjacency energy after deleting any of its edges,and finally get r-partite graph with the maximum anti-adjacency energy.In chapter 3,the anti-adjacency energy and inertia of three kinds of special graphs are studied.We get the minimum anti-adjacency energy of firefly graph,triangle ring graph with common point and complete graph with hanging point.