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Euler circuit

Definition 2 A Euler circuit is a circuit in a graph G that contains each edge of G exactly once. [Pg.10]

Euler theorem An undirected connected graph G has at least one Euler path if and only ifG has zero or two vertices of odd degree. If each vertex in G has even degree, then G has a Euler circuit. [Pg.11]

The 6-cycle Cq has two domains outer and inner. There are two cases either two 3-cycles lie in distinct domains, or both lie in the same, say, outer domain. In the first case, by symmetry, we can consider only the outer domain. The Euler formula shows that the boundary circuit of the cycle of 5-gons should have three tails. It is easy to verify that it is not possible to form a net of 6-gons using three tails of the 6-cycle and six tails of the 3-cycle. [Pg.176]

Graphs and electricity. After Euler the graph theory was rediscovered several times. In 1847 G. Kirchhoff developed the theory of trees to solve the problem about currents flowing in each conductor and in each loop of an electric circuit. Kirchhoff replaced the electric circuit by the graph and developed the procedure to solve the system of equations defining the current intensity, analysing only the so-called skeleton trees of the initial graph. [Pg.118]

Euler s relation (described in section 1.8) allows a relation to be drawn between the Euler characteristic (-x/N) per vertex to the average ring size (n) of rings on the surface, and the connectivity (z) of the atomic net on the surface. (A ring is defined to be the shortest circuit about a vertex along edges in the framework.) This relation is ... [Pg.60]


See other pages where Euler circuit is mentioned: [Pg.10]    [Pg.10]    [Pg.55]    [Pg.326]    [Pg.534]    [Pg.31]    [Pg.112]    [Pg.20]   
See also in sourсe #XX -- [ Pg.34 ]




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