Showing papers on "Split graph published in 1974"
16 May 1974
TL;DR: In this article, the authors introduce algebraic graph theory and show that the spectrum of a graph can be modelled as a graph graph, and the spectrum can be represented as a set of connected spanning trees.
Abstract: 1. Introduction to algebraic graph theory Part I. Linear Algebra in Graphic Thoery: 2. The spectrum of a graph 3. Regular graphs and line graphs 4. Cycles and cuts 5. Spanning trees and associated structures 6. The tree-number 7. Determinant expansions 8. Vertex-partitions and the spectrum Part II. Colouring Problems: 9. The chromatic polynomial 10. Subgraph expansions 11. The multiplicative expansion 12. The induced subgraph expansion 13. The Tutte polynomial 14. Chromatic polynomials and spanning trees Part III. Symmetry and Regularity: 15. Automorphisms of graphs 16. Vertex-transitive graphs 17. Symmetric graphs 18. Symmetric graphs of degree three 19. The covering graph construction 20. Distance-transitive graphs 21. Feasibility of intersection arrays 22. Imprimitivity 23. Minimal regular graphs with given girth References Index.
2,924 citations
TL;DR: In this paper, it was shown that a chordal graph G is a proper subtree graph, and an efficient algorithm for constructing a representation of G by a family of subtrees in a tree was given.
758 citations
TL;DR: In this paper, sufficient conditions for a graph to be Hamiltonian are given in terms of subgraph structure and do not require the fairly high global line density which is basic to the Posa-like sufficiency conditions.
56 citations
TL;DR: Acharya and Vartak as discussed by the authors characterized connected graphs and digraphs having an n th root and generalized results by Mukhopadhyay and D. P. Geller.
31 citations
TL;DR: In this article, upper and lower bounds for the number of vertices of the cliques of the critical graphs are obtained for any graph H such that H is the clique-graph of G.
18 citations
TL;DR: In this article, a tree-generation algorithm for cyclic graphs is presented, which, exploiting a canonical-lexical notational system, constructs the complete set of solutions in canonically increasing order, without redundancy.
2 citations
TL;DR: In this paper, all possible structures for the cutting center of a tree were determined and examples constructed which realize them, and they extended those results to all graphs, including all graphs with edges.
Abstract: The cutting number of a point of a connected graph is a measure of the extent to which the removal of that point cuts the graph. The cutting center of the graph is the set of points of maximal cutting number. In an earlier paper [1] all possible structures for the cutting center of a tree were determined and examples constructed which realize them. In this paper we extend those results to all graphs.
1 citations
01 Jan 1974
TL;DR: In this paper, it was shown that extremal graphs have a very simple and sYmmetric structure, and that the extremal graph is the graph of n vertices without subgraphs that isomorphic to the sample graph and has the maximum number of edges.
Abstract: The main result of this paper is that for a special, but rather wide class of "sample graphs", the extremal graphs, i.e, the graphs of n vertices without subgraphs isomorphic to the sample graph and having maximum number of edges under this condition, have very simple and sYmmetric structure. This result remains valid even in the case when the' condition "the graph does not contain the sample graph" is replaced by the condition "the graph does not contain the sample graph and its chromatic number is greater than t, where t is a fixed integer". The results of this paper have a lot of different applications, a few of which are listed in Section 3.