Self-dual non-Hamiltonian polyhedra with only two types of faces
Sharp sufficient conditions for Hamiltonian cycles in tough graphs
Shortness coefficient of cyclically 5-connected cubic planar graphs.
Shortness coefficient of cyclically 5-connected cubic planar graphs. (Short Communication).
Signed domination numbers of directed graphs
The concept of signed domination number of an undirected graph (introduced by J. E. Dunbar, S. T. Hedetniemi, M. A. Henning and P. J. Slater) is transferred to directed graphs. Exact values are found for particular types of tournaments. It is proved that for digraphs with a directed Hamiltonian cycle the signed domination number may be arbitrarily small.
Signed total -domination numbers of directed graphs.
Some graphic uses of an even number of odd nodes
Vertex-degree parity in large implicit “exchange graphs” implies some EP theorems asserting the existence of a second object without evidently providing a polytime algorithm for finding a second object.
Some new results about the shortness exponent in polyhedral graphs
Some properties of the zero divisor graph of a commutative ring
Let Γ(R) be the zero divisor graph for a commutative ring with identity. The k-domination number and the 2-packing number of Γ(R), where R is an Artinian ring, are computed. k-dominating sets and 2-packing sets for the zero divisor graph of the ring of Gaussian integers modulo n, Γ(ℤₙ[i]), are constructed. The center, the median, the core, as well as the automorphism group of Γ(ℤₙ[i]) are determined. Perfect zero divisor graphs Γ(R) are investigated.
Some remarks on Eulerian graphs
Some remarks on Jaeger's dual-hamiltonian conjecture
François Jaeger conjectured in 1974 that every cyclically 4-connected cubic graph is dual hamiltonian, that is to say the vertices of can be partitioned into two subsets such that each subset induces a tree in . We shall make several remarks on this conjecture.
Squares of triangular cacti
Strongly pancyclic and dual-pancyclic graphs
Say that a cycle C almost contains a cycle C¯ if every edge except one of C¯ is an edge of C. Call a graph G strongly pancyclic if every nontriangular cycle C almost contains another cycle C¯ and every nonspanning cycle C is almost contained in another cycle C⁺. This is equivalent to requiring, in addition, that the sizes of C¯ and C⁺ differ by one from the size of C. Strongly pancyclic graphs are pancyclic and chordal, and their cycles enjoy certain interpolation and extrapolation properties with...
Subsemi-Eulerian graphs.
Symmetric Hamilton Cycle Decompositions of Complete Multigraphs
Let n ≥ 3 and ⋋ ≥ 1 be integers. Let ⋋Kn denote the complete multigraph with edge-multiplicity ⋋. In this paper, we show that there exists a symmetric Hamilton cycle decomposition of ⋋K2m for all even ⋋ ≥ 2 and m ≥ 2. Also we show that there exists a symmetric Hamilton cycle decomposition of ⋋K2m − F for all odd ⋋ ≥ 3 and m ≥ 2. In fact, our results together with the earlier results (by Walecki and Brualdi and Schroeder) completely settle the existence of symmetric Hamilton cycle decomposition of...