Скачать или смотреть EULERIAN CIRCUIT AND TRAIL IN A GRAPH | GRAPH THEORY | DISCRETE MATHEMATICS

Eulerian Path is a path in graph that visits every edge exactly once. Eulerian Circuit is an Eulerian Path which starts and ends on the same vertex.

Eulerian Cycle
An undirected graph has Eulerian cycle if following two conditions are true.
….a) All vertices with non-zero degree are connected. We don’t care about vertices with zero degree because they don’t belong to Eulerian Cycle or Path (we only consider all edges).
….b) All vertices have even degree.
Eulerian Path
An undirected graph has Eulerian Path if following two conditions are true.
….a) Same as condition (a) for Eulerian Cycle
….b) If zero or two vertices have odd degree and all other vertices have even degree. Note that only one vertex with odd degree is not possible in an undirected graph (sum of all degrees is always even in an undirected graph)
Note that a graph with no edges is considered Eulerian because there are no edges to traverse.

Course : Discrete Mathematics
Semester : V
B.Sc (H) Mathematics
University of Delhi

Understand the notion of ordered sets and maps between ordered sets. Learn about lattices, modular and distributive lattices, sublattices and
homomorphisms between lattices. Become familiar with Boolean algebra, Boolean homomorphism, Karnaugh diagrams, switching circuits and their applications. Learn about basics of graph theory, including Eulerian graphs, Hamiltonian graphs. Learn about the applications of graph theory in the study of shortest path algorithms.

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