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Abstract:
In this paper an application of Euler line in hilla bridge and compare with k?nigsberg bridge and improve theorem in printor s problem / De Bruijn cycle are proposed, and the situation were r=4 and all possible of subsequence, its means all Euler line in directed graph are taken into consideration.
Introduction:
The basic idea of graphs were introduced in 18th centry by the great swiss mathematician leonhard Euler. He used graphs to solve the famous k?nigsberg bridge problem.German city of k?nigsberg(now it is Russian Kaliningrad)Was situated on the river Pregel.it had a park situated on the banks of the river and two islands .mainland and islands were joined by seven bridges.A problem was whether it was possible to take a walk through the town in such a way as to cross over every bridge once, and only once.
A graph is a set of points ( called vertices or nodes) connected by lines ( edges or arcs).
2-:Definition:1-A graph G=(V, E) consist of two sets ,set V of vertices and E of edges such that each e ? G can be identified with a pair (u,v) of vertices in V. the vertices u and v are known as end points of E.2-Awalk (w) in G is an alternative sequence of vertices and edges Repeatation of vertices and edges are allowed a walk is said to be an open walk if initial and end vertices are different otherwise w is closed.3-Atrail in G is an open walk without repeatation of edges .4-A path in G is an open walk without repeatation of vertices .5-A graph G is said to be an Euler graph if there is aclosed trail which covers all the edge of G.6-The degree of avertex is the number of edges incident on it . agraph is regular if all of its vertices have the same degree . i .e. if d ( v ) = k , ? v ?V then G is a k – regular.8-We say that G is connected if there is apath between each pair of vertices in G,if G is not connected it is disconnected graph .
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- Euler line in graph theory
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