By R. Balakrishnan, K. Ranganathan

ISBN-10: 1461445299

ISBN-13: 9781461445296

Graph idea skilled a huge development within the twentieth century. one of many major purposes for this phenomenon is the applicability of graph thought in different disciplines akin to physics, chemistry, psychology, sociology, and theoretical machine technological know-how. This textbook offers a high-quality historical past within the uncomplicated themes of graph concept, and is meant for a complicated undergraduate or starting graduate direction in graph theory.

This moment variation comprises new chapters: one on domination in graphs and the opposite at the spectral homes of graphs, the latter together with a dialogue on graph power. The bankruptcy on graph colors has been enlarged, overlaying extra issues reminiscent of homomorphisms and colors and the individuality of the Mycielskian as much as isomorphism. This e-book additionally introduces a number of fascinating issues akin to Dirac's theorem on k-connected graphs, Harary-Nashwilliam's theorem at the hamiltonicity of line graphs, Toida-McKee's characterization of Eulerian graphs, the Tutte matrix of a graph, Fournier's facts of Kuratowski's theorem on planar graphs, the evidence of the nonhamiltonicity of the Tutte graph on forty six vertices, and a concrete program of triangulated graphs.

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Extra resources for A Textbook of Graph Theory (2nd Edition) (Universitext)

Example text

Y; u/: C200 is a 44 Fig. T /; a contradiction. This proves the result. 3. Let T be a k-partite tournament, k 3: Then every vertex u belonging to a directed cycle in T must belong to either a directed 3-cycle or a directed 4-cycle. Proof. Let C be a shortest directed cycle in T that contains u: Suppose that C is not a directed 3-cycle. We shall prove that u is a vertex of a directed 4-cycle. 4. 2 states that every vertex of a diconnected tournament lies on a k-cycle for every k; 3 Ä k Ä n: However, this property is not true for a diconnected k-partite tournament.

4. If G is connected and E 0 is a set of edges whose deletion results in a disconnected graph, then E 0 contains an edge cut of G: It is clear that if e is a cut edge of a connected graph G; then G e has exactly two components. 5. Since the removal of a parallel edge of a connected graph does not result in a disconnected graph, such an edge cannot be a cut edge of the graph. A set of edges of a connected graph G whose deletion results in a disconnected graph is called a separating set of edges.

1. 4. If G is connected and E 0 is a set of edges whose deletion results in a disconnected graph, then E 0 contains an edge cut of G: It is clear that if e is a cut edge of a connected graph G; then G e has exactly two components. 5. Since the removal of a parallel edge of a connected graph does not result in a disconnected graph, such an edge cannot be a cut edge of the graph. A set of edges of a connected graph G whose deletion results in a disconnected graph is called a separating set of edges.

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A Textbook of Graph Theory (2nd Edition) (Universitext) by R. Balakrishnan, K. Ranganathan


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