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About Figure geodetic number of community

Author: ShiGuangLiang
Tutor: LvChangHong
School: East China Normal University
Course: Operational Research and Cybernetics
Keywords: Geodetic set Geodetic number Geodetic number on Distance
CLC: O157.5
Type: Master's thesis
Year: 2011
Downloads: 3
Quote: 0
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Abstract


Connected graph G, any two points u and v, a uv geodesic is u, v shortest path between two points . Orders Iu, v represents uv geodesic in the set of all points for a subset of S, Order I (S) = Uu.v ∈ SI (u, v), if I (S) = V (G), then we say S is a set of G geodetic . the measurement of G is called to set the minimum cardinality G geodetic number . Similarly, we can define the corresponding digraph D related concepts on all edges of G given a direction after drawing a graph G is called a directed graph , we call S (G) = {g (D): D is an orientation of a graph G is a graph G } geodetic number of spectra . g (G) = max S (G) of a graph G on the geodetic number. article discusses undirected graphs and digraphs geodetic number , the main contents are as follows : In the first chapter, we briefly introduce Figure geodesic set the background and some of the results already in the second chapter, we study the lower bound on the number of a geodesic conjecture: If G is a minimum degree of diameter d as δ nontrivial connected graph, then there is g (G) ≥ d δ. proved this conjecture three times the figure for non- , △ (G) ≤ 3 and unit area of the diagram Q diagram is correct in the third chapter, we first figure shows two complete graph with geodetic number on the Cartesian product of lower bounds on the map and geodetic number of geodetic number and size of the relationship a guess: for all graph has g (G) ≥ g (G). proved tree with full Cartesian product graphs satisfy g (G) ≥ g (G) and g (G) ≥ d △. also discussed the tree Cartesian product of complete graphs with geodetic number and d △ relationship in the fourth chapter , we give a block diagram of the geodetic number , and a block diagram of geodetic number range .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory
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