Showing papers on "Strongly regular graph published in 1990"
TL;DR: The algorithm is based on simulation of a rapidly convergent stochastic process, and runs in polynomial time for a wide class of degree sequences, including all regular sequences and all n -vertex sequences with no degree exceeding √ n /2.
138 citations
01 Mar 1990
TL;DR: This work closes up substantially the gaps between the known lower and upper bounds for these succinct problems, in most cases matching optimally the lower and the upper bound.
Abstract: Highly regular graphs can be represented advantageously by some kind of description shorter than the full adjacency matrix; a natural succinct representation is by means of a boolean circuit computing the adjacency matrix as a boolean function The complexity of the decision problems for several graph-theoretic properties changes drastically when this succinct representation is used to present the input We close up substantially the gaps between the known lower and upper bounds for these succinct problems, in most cases matching optimally the lower and the upper bound
48 citations
TL;DR: It is shown that there is a function ϵ(k) that tends to zero as k tends to infinity such that for every connected, k-regular simple graph G on n vertices C(G) = {k[1 − δ(G)]}n.
Abstract: Let C(G) denote the number of spanning trees of a graph G It is shown that there is a function ϵ(k) that tends to zero as k tends to infinity such that for every connected, k-regular simple graph G on n vertices C(G) = {k[1 − δ(G)]}n where 0 ≤ δ(G) ≤ ϵ(k)
34 citations
01 Jan 1990
TL;DR: A data structure that supports insertion and regular path existence queries inO(nk2) amortized time andO(|F|) worst-case time, respectively is presented and it is shown how this data structure and the techniques used for building it are applicable to the area of knowledge base querying.
Abstract: If $G$ is a directed graph with labeled edges and $L$ is a fixed regular language, the {\em regular path problem}, given two nodes, $u$ and $v$, in $G$, is to find a path between $u$ and $v$ such that the labels on the arcs along that path form a string which is a member of $L$. We consider a dynamic version of this problem, adding arcs to and performing regular path queries on $G$ over $L$, and present a data structure that solves both problems in average time per operation linear in the number of nodes of the graph for any fixed regular language.
18 citations
TL;DR: The linear arboricity la(G) of a graph G is the least number of linear forests required to cover the edges of G, which is equivalent to the assertion that for every r-regular graph G.
Abstract: A linear forest is a forest in which each connected component is a path. The linear arboricity la(G) of a graph G is the least number of linear forests required to cover the edges of G. The linear arboricity conjecture is equivalent to the assertion that for every r-regular graph G
17 citations
DOI•
01 Jan 1990
TL;DR: A submitted manuscript is the author's version of the article upon submission and before peer-review as discussed by the authors, and the final published version features the final layout of the paper including the volume, issue and page numbers.
Abstract: • A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.
15 citations
TL;DR: This paper presents one way of constructing completely regular binary block-codes taking one kind of distance-regular graph as a starting point, and uses some well-known results concerning this type of code in order to find a solution to the problem of classifying the given graphs.
12 citations
TL;DR: A related property—being strongly critical —that is satisfied by many critical graphs, including complete graphs, are considered, and the Dirac join operation preserves both amenability and the strongly critical property.
11 citations
TL;DR: It is shown that if m ⩽ 2 is an even integer and G is a graph such that dG(v) ⩾ m + 1 for all vertices v in G, then the line graph L(G) of G has a 2m-factor.
10 citations
TL;DR: The path layer matrix (or path degree sequence) of a graph G contains quantitative information about all paths in G, where Elements (i, j) in this matrix is the number of simple paths inG having initial vertex v i and length j.
Abstract: The path layer matrix (or path degree sequence) of a graph G contains quantitative information about all paths in G. Elements (i, j) in this matrix is the number of simple paths in G having initial vertex v i and length j. For every r≥3, pairs of nonisomorphic r-regular graphs having the same path layer matrix are presented
8 citations
Posted Content•
TL;DR: In this paper, the authors studied symmetric designs with a polarity for which the graph induced by the absolute points and the graph generated by the non-absolute points both are strongly regular.
Abstract: We study symmetric designs with a polarity for which the graph induced by the absolute points and the graph induced by the non-absolute points both are strongly regular. The main result ís that all parameters can be expressed in terms of only one parameter.
TL;DR: The minimum number of edges in a regular connected graph on n vertices, containing a complete subgraph of order k ≤ n/2, is determined, enabling us to confirm and strengthen a conjecture of P. Erdos on the existence of regular graphs with prescribed chromatic number.
Abstract: We determine the minimum number of edges in a regular connected graph on n vertices, containing a complete subgraph of order k ≤ n/2. This enables us to confirm and strengthen a conjecture of P. Erdos on the existence of regular graphs with prescribed chromatic number.
TL;DR: In this paper, the concept of Propelinear Code was introduced, which is the algebraic structure associated to an e-Latticed, Distance-Regular Graph, and it was shown that such a graph cannot be represented by a complete regular code.
Abstract: In [5] we established some relations between Distance Regular Graphs and Completely-Regular Codes in order to show the non-existence of a class of Distance-Regular Graph. In [6] we introduced the concept of Propelinear Code which is the algebraic structure associated to an e-Latticed, Distance-Regular Graph.
TL;DR: This work has shown that any pair of vertices in a 4-connected non-bipartite k -regular graph are joined by a Hamilton path or a path of length at least 3 k −6.
TL;DR: Bill Jackson has proved that every 2-connected, k -regular graph on at most 3 k vertices is hamiltonian and it is shown that, under almost the same conditions, the graphs are edge-hamiltonian.
TL;DR: In this paper, the concept of lexically ordered adjacency matrix of a graph is introduced and it is proved that every adjACency matrix is isomorphic to at least one lexical ordered matrix.
Abstract: The concept of lexically ordered adjacency matrix of a graph is introduced and it is proved that every adjacency matrix is isomorphic to at least one lexically ordered adjacency matrix. An algorithm for the classification of strongly regular graphs is developed, where the property of lexical ordering is used as a means to reduce the number of generated adjacency matrices. We also describe other pruning methods that can be used.
TL;DR: The maximum numbers of mutually nonadjacent vertices in a family of strongly regular graphs arising from orthogonal geometries overGF(2) are expressed in terms of the classical Hurwitz-Radon numbers and their generalizations.
Abstract: The maximum numbers of mutually nonadjacent vertices in a family of strongly regular graphs arising from orthogonal geometries overGF(2) are expressed in terms of the classical Hurwitz-Radon numbers and their generalizations.
01 Jan 1990
TL;DR: In this article, the authors construct self-orthogonal binary codes from projective 2 - (v, k, λ) designs with a polarity, k odd, and λ even.
Abstract: We construct self-orthogonal binary codes from projective 2 - (v, k, λ) designs with a polarity, k odd, and λ even. We give arithmetic conditions on the parameters of the design to obtain self-dual or doubly even self-dual codes. Non existence results in the latter case are obtained from rationality conditions of certain strongly regular graphs.
TL;DR: The number of non-isomorphic (p, n)-packed graphs is obtained by solving the inequality of the following type: For α ≥ 1, β ≥ 1 using LaSalle's inequality.