Description: A quotient graph is formed by partitioning the vertices of a graph into disjoint subsets and treating each subset as a single vertex. This concept is fundamental in graph theory as it allows for the simplification of a graph’s structure by grouping vertices that share certain properties or relationships. In a quotient graph, the edges between the new vertices (subsets) are defined based on the edges that existed between the original vertices. This means that if there is at least one edge connecting two vertices from different subsets, an edge is drawn between the corresponding vertices of the quotient graph. This representation is useful for studying global properties of the original graph, as it reduces complexity by working with fewer vertices. Additionally, quotient graphs can be used to analyze hierarchical or equivalence relationships, facilitating the visualization and understanding of complex structures. In summary, quotient graphs are a powerful tool in graph theory that allows for the simplification and analysis of relationships in interconnected data sets.
