By R. Balakrishnan, K. Ranganathan

ISBN-10: 1441985050

ISBN-13: 9781441985057

ISBN-10: 1461264227

ISBN-13: 9781461264224

This moment variation contains new chapters: one on domination in graphs and the opposite at the spectral houses of graphs, the latter including a dialogue on graph energy. The bankruptcy on graph colours has been enlarged, protecting extra subject matters corresponding to homomorphisms and shades and the individuality of the Mycielskian as much as isomorphism.

This publication additionally introduces a number of attention-grabbing subject matters comparable 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 evidence of Kuratowski's theorem on planar graphs, the evidence of the nonhamiltonicity of the Tutte graph on forty six vertices, and a concrete software of triangulated graphs.

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**Additional info for A Textbook of Graph Theory**

**Example text**

Then G contains no cut vertex . Let u and v be two distinct vertices of G. We now use induction on d(u , v) to prove that u and v are joined by two internally disjoint paths. If d(u , v) = 1, let e = uv. As G is 2-connected and n(G ) 2: 3, e cannot be a cut edge of G , since if e were a cut edge , at least one of u and v must be a cut vertex. 7 , e belongs to a cycle C in G . Then C-e is a u-v path in G, internally disjoint from the path uv. 52 III. 8. 7 Now assume that any two vertices x and y of G, such that d (x , y) = k - I , k 2: 2, are joined by two internally disjoint x-y paths in G .

Then C-e is a u-v path in G, internally disjoint from the path uv. 52 III. 8. 7 Now assume that any two vertices x and y of G, such that d (x , y) = k - I , k 2: 2, are joined by two internally disjoint x-y paths in G . Let d(u , v) = k. Let P be a u-v path of length k and w be the vertex of G just preceding v on P. Then d(u , w) = k - l. By induction hypothesis, there are two internally disjoint u-w paths , say PI and Pz, in G . As G has no cut vertex, G-w is connected and hence there exists a u-v path Q in G-w .

3 subgraph of G onto a K 1,3 subgraph of G' . 3 subgraph of G . 24. 24. Graphs with five verticesand edge e adjacent to one or all three other edges 24 I. 3 subgraph or a triangle in G'. If ¢ I (el ), ¢, (e2), and ¢1(e3) form a triangle in G', ¢I (e) can be adjacent to preci sely two of ¢I (e, ), ¢1(e2), and ¢1(e3) (since L (G ' ) is simple), whereas ¢I (e) must be adjacent to only one or all the three . This contrad iction shows that {¢I (el), ¢I (e2), ¢I (e3 )} is not a triangle in G' and therefore form s a K 1,3 in G'.

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

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