Description: A quasi-bipartite graph is a type of graph that resembles a bipartite graph but has a distinctive feature: it allows the existence of some edges connecting vertices within the same set. In a bipartite graph, vertices are divided into two disjoint sets such that there are no edges between vertices of the same set. However, in a quasi-bipartite graph, this restriction is relaxed, meaning that there can be some edges connecting vertices within one or both of the sets. This property makes quasi-bipartite graphs useful in various applications where some flexibility in the connection of nodes is required. Quasi-bipartite graphs can be represented using an adjacency matrix, where the arrangement of vertices and the edges connecting them can be observed. Classifying a graph as quasi-bipartite can be useful in the analysis of networks, where groups of entities may have connections both within their own group and with other groups. In summary, quasi-bipartite graphs are an extension of bipartite graphs that allow for greater complexity in the relationships between vertices, making them an interesting object of study in graph theory.
