Some Results On The Geodetic Number Of Graph

The geodetic number of graphs is an important parameter revealing the structural character of graphs. The geodetic number of graphs originated from the convex set theory of geometry, topology and functional analysis and is the generalization and application of convex set theory in graph theory.In this thesis, we will consider the geodetic number of graphs and disgraphs, and research results of mine are mainly Presented.the main content of the thesis involves the following three parts:1,Some properties about the geodetic set of graphs and their orientations.2,The geodetic number and the geodetic set of the General Mycielski of Path,Cycle,Star.3,study futher the relation of the geodetic number and the geodetic spectrum ofsome graph.The main results of this paper:1,M_p(P_n) is the General Mycielski Graph of path P_n, then:2,M_p(C-n) is the General Mycielski Graph of cycle C_n, then:3,m_p(T_n) is the General Mycielski Graph of star T_n (n≥3), then:4,M_p (K_n) is the General Mycielski Graph of K_n (n≥3), then: g(M_p(K_n) = 2n5,If G is a 2-connected graph, and X, Y are disjoint subset of G ,and each of them contains at least two verteic, then 2∈S(G) 6,If G is a connected, simple graph, and |V(G)|>2δ, then:8,let C_n,C_m be two cycle,C_n,C_m joining atÏ…₁ andÏ…₂,denotedby C_{Ï…1,Ï…2} and the geodetic spectrum of C_{Ï…1,Ï…2} is:...