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
,
preprint,
available as pdf-file.
(with A.A. Delgado) Perfect domination in rectangular
grid graphs
, to appear during 2008 in JCMCC,
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 to appear in JCMCC, available as
pdf-file, with a kind contribution by
Elizabeth Billington.
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 that appear in this
paper, appear also in the literature as perfect codes in Lee metric, starting in the
paper of
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 proved the mentioned nonexistence conjecture for d=4.)
