Any graph produced in this way will have an important property. The notes form the base text for the course mat62756 graph theory. The linked list representation has two entries for an edge u,v, once in the list for u and once for v. E consists of a nite set v and a set eof twoelement subsets of v. They contain an introduction to basic concepts and results in graph theory, with a special emphasis put on the networktheoretic circuitcut dualism. Combinatorics and graph theory, second edition undergraduate. If the vertices are already present, only the edges are added. A spanning tree of a graph is just a subgraph that contains all the vertices and is a tree. What is the common link between the following problems. Given a graph or a directed graph, does there exist a cycle in the graph that contains each vertex once. The elements of v are called vertices and the elements of eare called. All 16 of its spanning treescomplete graph graph theory s sameen fatima 58 47.
Hamilton 180565 led to the concept of a hamiltonian graph. Undirected graph for an undirected graph the adjacency matrix is symmetric, so only half the matrix needs to be kept. We call g connected if there is a path between any two distinct vertices of g. Show that if all cycles in a graph are of even length then the graph is bipartite. Odessa seminar on graph theory, organised by aleksandr aleksandrovich. An introduction to combinatorics and graph theory whitman college. Graph theory is a delightful playground for the exploration of proof tech niques in. The feud between the montagues and the capulets of verona has been well doc. No appropriate book existed, so i started writing lecture notes. Graph theory history the origin of graph theory can be traced back to eulers work on the konigsberg bridges problem 1735, which led to the concept of an eulerian graph. Simple graphs are graphs without multiple edges or selfloops. Cs6702 graph theory and applications notes pdf book anna university semester. Euler paths consider the undirected graph shown in figure 1. The dots are called nodes or vertices and the lines are called edges.
The lecture notes are loosely based on gross and yellens graph theory and its appli. Nonplanar graphs can require more than four colors, for example this graph this is called the complete graph on ve vertices, denoted k5. In recent years, graph theory has established itself as an important mathematical tool in a wide variety of subjects, ranging from operational research and chemistry to genetics and linguistics, and from electrical engineering and geography to sociology and architecture. Cs6702 graph theory and applications notes pdf book slideshare. Color the edges of a bipartite graph either red or blue such that for each node the number of incident edges of the two colors di. Graph theory is concerned with various types of networks, or really models of networks called graphs. Samatova department of computer science north carolina state university and computer science and mathematics division oak ridge national laboratory. Graph theory free download as powerpoint presentation.