By R. Balakrishnan, K. Ranganathan

ISBN-10: 1461445280

ISBN-13: 9781461445289

ISBN-10: 1461445299

ISBN-13: 9781461445296

Graph concept skilled an immense progress within the twentieth century. one of many major purposes for this phenomenon is the applicability of graph thought in different disciplines similar to physics, chemistry, psychology, sociology, and theoretical computing device technological know-how. This textbook presents a superior heritage within the simple subject matters of graph thought, and is meant for a sophisticated undergraduate or starting graduate direction in graph theory.

This moment version contains new chapters: one on domination in graphs and the opposite at the spectral homes of graphs, the latter together with a dialogue on graph strength. The bankruptcy on graph hues has been enlarged, protecting extra subject matters corresponding to homomorphisms and colours and the distinctiveness of the Mycielskian as much as isomorphism. This ebook additionally introduces numerous attention-grabbing subject matters reminiscent of 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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Additional resources for A Textbook of Graph Theory

Example text

U; v/; u is called the tail of a; and v is the head of a: The arc a is said to join v with u: u and v are called the ends of a: A directed graph is also called a digraph. D/ when reference to D is needed) on the same vertex set as follows: Corresponding to each arc of D; there is an edge of G with the same ends. This graph G is called the underlying graph of the digraph D: Thus, every digraph D defines a unique (up to isomorphism) graph G: Conversely, given any graph G; we can obtain a digraph from G by specifying for each edge of G an order of its ends.

V/ D d. 1). 6 Automorphism of a Simple Graph 19 Fig. u7 / D u7 on degree consideration. 2. 3. 4. 5. v// D N. 7 Line Graphs Let G be a loopless graph. G/, and hence we assume in this section that G has no isolated vertices. We also assume that G has no loops. G/ of a graph G follow: 1. G/ is connected. 2. G/: 3. G/: 4. v/ 2: 5. G/ v1 e1 v2 e2 v4 e4 e5 e3 e7 v7 v3 v6 e6 v5 G Fig. 1. 2. 1. The line graph of a simple graph G is a path if and only if G is a path. Proof. Let G be the path Pn on n vertices.

There are graphs at the other extreme as well, such as the complete graphs Kn ; n 2; which remain connected after the removal of any k vertices, 1 Ä k Ä n 1: Consider a communication network. Any such network can be represented by a graph in which the vertices correspond to communication centers and the edges represent communication channels. In the communication network of Fig. 1a, any disruption in the communication center v will result in a communication breakdown, whereas in the network of Fig.

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A Textbook of Graph Theory by R. Balakrishnan, K. Ranganathan

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