Showing papers on "Strongly regular graph published in 1978"
TL;DR: In this paper, the Bose-Mesner algebra of a strongly regular graph Γ is reviewed, and a special basis relative to some vertex of the graph is presented in the i th eigenspace V i, i ∈ {1, 2}.
156 citations
TL;DR: This work poses the problem of determining the Ramsey numbers r(Bm, Bn) and demonstrates that in many cases critical colorings are avialable from known examples of strongly regular graphs.
Abstract: For n = 1, 2, …, let Bn = K2 + Kn. We pose the problem of determining the Ramsey numbers r(Bm, Bn) and demonstrate that in many cases critical colorings are avialable from known examples of strongly regular graphs.
65 citations
TL;DR: It is shown that line connectivity is a crucial property for characterizing regular magic graphs and, in fact, bipartite graphs are magic if and only if λ(G)≠2.
50 citations
TL;DR: In this article, the authors examine computing techniques applicable to the construction and analysis of combinatorial configurations and present some original generation techniques as well as new results on properties of these graphs.
Abstract: In this paper we examine computing techniques applicable to the construction and analysis of combinatorial configurations. These techniques are first described for arbitrary configurations and then elaborated for a particular example. The generation procedures which are reviewed are backtracking and hill-climbing. In order to analyse a configuration it is often necessary to employ heuristic algorithms since the properties to be determined constitute an NP-complete problem. Various heuristic strategies are discussed for such analyses. The example consists of the family of strongly regular graphs with parameter sets (25, 12, 5, 6) and (26, 10, 3, 4). For these strongly regular graphs we present some original generation techniques as well as new results on properties of these graphs.
31 citations
TL;DR: A one-to-one correspondence between BIBD's with k = 3 and λ = 2 and triangulation systems for complete graphs is established and a process is developed for “doubling” a given PBIBD of an appropriate form.
25 citations
TL;DR: In this paper, it was shown that a two-connected (m − k)-regular graph G of order 2m is Hamiltonian if k(≥1) is sufficiently small.
Abstract: Publisher Summary This chapter presents the theorem of Hamiltonian cycles in regular graphs. If in a graph of order n every vertex has degree at least 1/2n then the graph contains a Hamiltonian cycle. This theorem is the first in a long line of results concerning forcibly Hamiltonian degree sequences—that is, degree sequences all whose realizations are Hamiltonian. A question is discussed whether a two-connected (m – k)-regular graph G of order 2m is Hamiltonian if k(≥1) is sufficiently small. If instead of regularity we ask only that the minimal degree is m – 1 then the answer is negative. The order of k in the example above is best possible: the graph has to be Hamiltonian if k
24 citations
TL;DR: This paper extends the class of graphs H such that if G0 = H, for some point determining graph G, then G has a 1-factor.
2 citations
TL;DR: This paper established the form of the conjecture that every undirectefl regular graph, except the complement of a complete graph, has at least two disjoint maximal independent sets of vertices for regular graphs of degree.
1 citations