On non-separating embeddings of graphs in closed surfaces.
On non-z(mod k) dominating sets
For a graph G, a positive integer k, k ≥ 2, and a non-negative integer with z < k and z ≠ 1, a subset D of the vertex set V(G) is said to be a non-z (mod k) dominating set if D is a dominating set and for all x ∈ V(G), |N[x]∩D| ≢ z (mod k).For the case k = 2 and z = 0, it has been shown that these sets exist for all graphs. The problem for k ≥ 3 is unknown (the existence for even values of k and z = 0 follows from the k = 2 case.) It is the purpose of this paper to show that for k ≥ 3 and with...
On Norm Three Vectors in Integral Euclidean Lattices. I.
On normal partitions in cubic graphs
A normal partition of the edges of a cubic graph is a partition into trails (no repeated edge) such that each vertex is the end vertex of exactly one trail of the partition. We investigate this notion and give some results and problems.
On number of commutative mappings from finite set into itself (Preliminary communication)
On number of covering arcs in orderings
On odd and semi-odd linear partitions of cubic graphs
A linear forest is a graph whose connected components are chordless paths. A linear partition of a graph G is a partition of its edge set into linear forests and la(G) is the minimum number of linear forests in a linear partition. In this paper we consider linear partitions of cubic simple graphs for which it is well known that la(G) = 2. A linear partition is said to be odd whenever each path of has odd length and semi-odd whenever each path of (or each path of ) has odd length. In [2] Aldred...
On open Hamiltonian walks in graphs
On optimal linear codes over .
On optimal play in the game of Hex.
On Optimal Realizations of Finite Metric Spaces by Graphs.
On order and geodesic alignment of a connected bigraph
On order statistics for random sample size having compound binomial and Poisson distributions
On oriented graph scores
On orthogonal Latin -dimensional cubes
We give a construction of orthogonal Latin -dimensional cubes (or Latin hypercubes) of order for every natural number and . Our result generalizes the well known result about orthogonal Latin squares published in 1960 by R. C. Bose, S. S. Shikhande and E. T. Parker.
On (p, 1)-total labelling of 1-planar graphs
A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ(G) ≥ 8p+4 or Δ(G) ≥ 6p+2 and g(G) ≥ 4. As a consequence, the well-known (p, 1)-total labelling conjecture has been confirmed for some 1-planar graphs.
On -binomial coefficients.
On P4-tidy graphs.
On packing densities of permutations.
On packing spheres into containers.