Some Results On The Generalized Cacti Graphs

A graph is called to be generalized cacti if each of its blocks is an edge,a cycle or a bicyclic graph.In this paper,we mainly study the extremal problems of spanning tree and matching energy of generalized cacti graphs.First,we determine the graphs achieving the minimum matching energy in generalized cacti graphs and generalized cacti bipartite graphs.Secendly,we determine the graphs achieving the minimum tree number in generalized cacti graphs and generalized cacti bipartite graphs.