Showing papers on "Petersen graph published in 1981"
TL;DR: A graph having 27 vertices is described, whose automorphism group is transitive on vertices and undirected edges, but not on directed edges.
Abstract: A graph having 27 vertices is described, whose automorphism group is transitive on vertices and undirected edges, but not on directed edges.
97 citations
73 citations
TL;DR: It is shown that certain conditions assumed on a regular self-complementary graph are not sufficient for the graph to be strongly regular, answering in the negative a question posed by Kotzig in [1].
Abstract: It is shown that certain conditions assumed on a regular self-complementary graph are not sufficient for the graph to be strongly regular, answering in the negative a question posed by Kotzig in [1].
5 citations
TL;DR: In this paper, it was shown that the Graph Reconstruction Conjecture is equivalent to a conjecture about the algebraic properties of directed trees and their homomorphic images, which is called the Kelly-Ulam conjecture.
2 citations
TL;DR: In this paper, the connexion among graph enumerating polynomials and graph reconstruction from point-deleted subgraphs or edge-deletion partial graphs is studied.
Abstract: In this paper we study the connexion among graph enumerating polynomials and then we prove for these polynomials theorems concerning the reconstruction of a graph from its point-deleted subgraphs or edge-deleted partial graphs.
1 citations
1 Jan 1981
TL;DR: In this article, a family of hypo-hamiltonian generalized prisms with 4k+2 vertices k≠1,3 was constructed, which gave us new cubic-hypohamiltonian graphs for k>5.
Abstract: In this paper we construct a family of hypo-hamiltonian generalized prisms with 4k+2 vertices k≠1,3. This family gives us new cubic-hypohamiltonian graphs for k>5.
1 citations
TL;DR: In this article, four bounds for the chromatic number have been calculated for several graphs, and the same method was the best for every graph for each graph, but not for all graphs.
Abstract: Four bounds for the chromatic number have been calculated for several graphs. The same method was the best for every graph.
TL;DR: The following are proved: let G be a graph with e"G edges, which is (k - 1)-edge- connected, and with all valences >=k, and the proof is based on a useful extension of Tutte's factor theorem.
TL;DR: It is shown that for each fixed $n \geqq 3$ it is NP-complete to determine whether an arbitrary graph can be edge-partitioned into subgraphs isomorphic to the complete graph K_n.
Abstract: We show that for each fixed $n \geqq 3$ it is NP-complete to determine whether an arbitrary graph can be edge-partitioned into subgraphs isomorphic to the complete graph $K_n $. The NP-completeness of a number of other edge-partition problems follows immediately.