Showing papers on "Strongly regular graph published in 1977"
TL;DR: The following is proved: If G is graph of order p (≥2) and size p-2, then there exists an isomorphic embedding of G into its complement.
Abstract: The following is proved: If G is graph of order p (≥2) and size p-2, then there exists an isomorphic embedding of G into its complement.
56 citations
TL;DR: This initial study of k-critical graphs is concerned with the problem of determining the values of n and k for which there exists an (n∗, k∗) graph.
31 citations
TL;DR: In this article, it was shown that the existence of a perfect e-code in a halved graph T is equivalent to a uniformly packed 2e-code with certain specific parameters.
Abstract: For each bipartition_of a bipartite distance-regular graph F, there naturally corresponds another distance-regular graph F called a halved graph. It is shown that the existence of a perfect e-code in a halved graph F is equivalent to the existence of a uniformly packed 2e-code in F with certain specific parameters. Using this equivalence, we show the non-existence of perfect codes for two classes of distance-regular graphs F corresponding to F = Qk and F = 2. Ok. For the basic definitions and properties of distance-regular graphs, the reader is referred to Biggs [2]. Let T be a distance-regular graph with distance function d and intersection array '\" 1 r r r\\ 1 L2 ... < d i C 1). We say that C has external distance (i.e. the true external distance in the sense of Delsarte [3]) e + m if the maximal distance of any vertex of F from C is e+m. We choose zi (e V(T), the set of vertices of F) such that d(zj, C) = j (where j e {0, 1, ..., e+m}) and call C completely regular if the numbers |{xeC| d(x,zj) = i}\\ = Pij(C,zj) = py(C) (where ie{0, 1, ...}d} and j e {0, 1, ..., e + m}) depend only on i and j and not on the choice of Zj. We say that C is locally regular if the numbers py(C,zj) = Pij(C) (where i , je{0, 1, ...}e+m}) depend only on i and ; and not on the choice of zy It is proved that a locally regular Received 5 November, 1976. [J. LONDON MATH. SOC. (2), 16 (1977), 197-202]
16 citations
TL;DR: This paper proves that if k is an integer no less than 3, and if G is a two-connected graph with 2n a vertices, a E {0, 1}, which is regular of degree n k, then G is Hamiltonian.
12 citations
TL;DR: An interesting corollary of the structure theorem is that if G is a s.c. graph of order p⩾8 with minimum degree at least p 4 , then G has a 2-factor and the result is the best possible.
11 citations
TL;DR: In this paper, it was shown that if G is a connected graph with δ(G) ≥ 3, where δ denotes the minimum degree of G, then L2(G), where G is 2-connected and G ≥ 4, is (2δ (G) − 4)-Hamiltonian.
7 citations
TL;DR: The purpose of this note is to add some examples of groups which have a graphical regular representation.
2 citations
TL;DR: The connected graphs G which are regular of valence n and in which for all adjacent vertices x and y | Δ ( x ) ∩ Δ ( y )| = n − 1 − s are described.
1 citations
TL;DR: The conjecture that if all distance trees of G are isomorphic to each other then G is a regular graph, is settled affirmatively.
1 citations
TL;DR: In this note, some properties of E -minimal graphs are given.