Interrelations between
Graph Theory, Combinatorial Designs, Coding Theory,
Applied Algebra, Geometry and Topology.
Symmetry-search viewpoint
in algebraic structures, including hypercubes, Cayley graphs and other colored
structures found in codes and designs,
finite fields and geometries.
At present, involved in geometric and combinatorial properties
of perfect error-correcting codes and related domination and
algebraic graph theory topics.
Distribution of Distances in Star Graphs
,
preprint,
available as pdf-file.
Great Circle Challenge and Odd Graphs
,
preprint,
available as pdf-file.
(with A.A. Delgado) Classes of Hamilton Cycles in the 5-Cube
, JCMCC 61 (2007), 81-95, available as pdf-file.
(NOTE: Reference [3]
at the end of this paper can be found in
http://home.coqui.net/dejterij/mcns/mirame.txt),
as the original site http://www.cnnet.edu became defunct.
On a {K_4,K_{2,2,2}}-ultrahomogeneous graph
,
Australasian Journal of Combinatorics, 44(2009), 63-75.
preprint available as pdf-file.
(with A.A. Delgado)
Perfect domination in rectangular
grid graphs
, to appear in JCMCC, volume 70, August 2009,
available as pdf-file.
A larger version of this manuscript
is available here
(with C. C. Lindner, C. A. Rodger and M. Meszka) Almost resolvable 4-cycle systems
,
JCMCC, 63 (2007), 173 - 182,
available as pdf-file;
with a Corrigendum/Addendum in JCMCC, 66 (2008), 297-298, available as
pdf-file, containing a kind contribution by
Elizabeth Billington: using the corrected Example 2.1, contributed by Dejter,
that provided an almost resolvable 4-cycle system of order n = 17, to construct
one of the missing cases, namely the one whose order is n = 33.
(Cases n = 41 and 57 are still not known).
Perfect domination in regular grid graphs,
Australasian Journal of Combinatorics, 92 (2008), 99-114,
available as pdf-file, by courtesy of
http://ajc.maths.uq.edu.au. (M. Mollard, indicated recently that the
1-perfect codes in this paper, appear also in the literature
as perfect codes in Lee metric, starting with the paper by
S. Golomb and K. Welch, Perfect codes in Lee metric
and the packing of polyominoes, SIAM J. Appl. Math.
18 (1970) 302-317, who proved
their existence in all dimensions, as in Theorem 13. Mollard also
mentioned that d-perfect codes (d>1) have been studied in the
2-dimensional grid; their nonexistence have been conjectured for larger
dimensions, proved for d=3 in S. Gravier, M. Mollard and C. Payan,
On the non-existence of 3-dimensional tiling
in the Lee metric, Eur. J. Combin. 19 (1998) 567-572.
By the same authors: Variation on tilings
in Manhattan metric, Geom. Dedicata 76 (1999) 265-273,
On the nonexistence of three-dimensional
tiling in the Lee metric II, Discrete Math., 235 (2001)
151-157. S. Spacapan Non-existence of face-to-face
four dimensional tiling in the Lee metric, European J. Combin. 28 (2007)
127,133, proved the mentioned nonexistence conjecture
for d=4. P. Horak, Tilings in Lee Metric,
Eur. J. Combin., 30(2009), 480-489, has
a shorter proof of this and extends it for d=5).
Quasiperfect domination in triangular
lattices, Discussiones Mathematicae Graph Theory, 29(1) (2009), 179-198,
available here as pdf-file.
SQS-graphs of Solov'eva-Phelps codes, preprint,
available as pdf-file.
On certain $\mathcal C$-ultrahomogeneous graphs obtained from cubic distance transitive graphs codes, preprint,
available as pdf-file.
On a $\vec{C}_4$-ultrahomogeneous digraph, preprint,
available as pdf-file.
