Quotient graph Definition 13: Suppose G(VE) is a graph and R is a equivalence relation on the set V. we construct the quotient graph gR in the follow way. The vertices of GR are the equivalence classes of v produced by r If v and w are the equivalence classes of vertices v and w of G, then there is an edge in g between v and w if some vertex in v] is connected to some vertex in w in the graph G
❖Quotient graph ❖ Definition 13: Suppose G(V,E) is a graph and R is a equivalence relation on the set V. We construct the quotient graph GR in the follow way. The vertices of GR are the equivalence classes of V produced by R. If [v] and [w] are the equivalence classes of vertices v and w of G, then there is an edge in GR between [v] and [w] if some vertex in [v] is connected to some vertex in [w] in the graph G
5.2 Paths and circuits .8.5.2.1 Paths and circuits % Definition 14: Let n be a nonnegative integer and g be an undirected graph. A path of length n from u to y in G is a sequence of edges elsey,en of G such that e=vo=u, V1, e2=v1,V2,,en=vn-1,Vn=v), and no edge occurs more than once in the edge sequence. When G is a simple graph, we denote this path by its vertex sequence u=vo V1.Vn-V. A path is called simple if no vertex appear more than once. A circuit is a path that begins and ends with the same vertex. A circuit is simple if the vertices V1,V2,.,Vn-I are all distinct
5.2 Paths and Circuits ❖5.2.1 Paths and Circuits ❖ Definition 14: Let n be a nonnegative integer and G be an undirected graph. A path of length n from u to v in G is a sequence of edges e1 ,e2 ,…,en of G such that e1={v0=u,v1 }, e2={v1 ,v2 },…,en={vn-1 ,vn=v}, and no edge occurs more than once in the edge sequence. When G is a simple graph, we denote this path by its vertex sequence u=v0 ,v1 ,…,vn=v. A path is called simple if no vertex appear more than once. A circuit is a path that begins and ends with the same vertex. A circuit is simple if the vertices v1 ,v2 ,…,vn-1 are all distinct