86 research outputs found
Small cycles, generalized prisms and Hamiltonian cycles in the Bubble-sort graph
The Bubble-sort graph , is a Cayley graph over the
symmetric group generated by transpositions from the set . It is a bipartite graph containing all even cycles of
length , where . We give an explicit
combinatorial characterization of all its - and -cycles. Based on this
characterization, we define generalized prisms in , and
present a new approach to construct a Hamiltonian cycle based on these
generalized prisms.Comment: 13 pages, 7 figure
Reconstruction of permutations distorted by single transposition errors
The reconstruction problem for permutations on elements from their
erroneous patterns which are distorted by transpositions is presented in this
paper. It is shown that for any an unknown permutation is uniquely
reconstructible from 4 distinct permutations at transposition distance at most
one from the unknown permutation. The {\it transposition distance} between two
permutations is defined as the least number of transpositions needed to
transform one into the other. The proposed approach is based on the
investigation of structural properties of a corresponding Cayley graph. In the
case of at most two transposition errors it is shown that
erroneous patterns are required in order to reconstruct an unknown permutation.
Similar results are obtained for two particular cases when permutations are
distorted by given transpositions. These results confirm some bounds for
regular graphs which are also presented in this paper.Comment: 5 pages, Report of paper presented at ISIT-200
An improved bound on the chromatic number of the Pancake graphs
In this paper an improved bound on the chromatic number of the Pancake graph
, is presented. The bound is obtained using a subadditivity
property of the chromatic number of the Pancake graph. We also investigate an
equitable coloring of . An equitable -coloring based on efficient
dominating sets is given and optimal equitable -colorings are considered for
small . It is conjectured that the chromatic number of coincides with
its equitable chromatic number for any
The Wiener Polynomial Derivatives and Other Topological Indices in Chemical Research
Wiener polynomial derivatives and some other information and topological indices are investigated with respect to their discriminating power and property correlating ability
ΠΠ²Π° ΡΠ»ΡΡΠ°ΡΠ° Π½Π° Π½Π΅ΡΠΈΠ½Π΄ΡΠΎΠΌΡΠΊΠ° ΠΊΠΎΠ½Π³Π΅Π½ΠΈΡΠ°Π»Π½Π° ΡΠ½ΠΈΠ»Π°ΡΠ΅ΡΠ°Π»Π½Π° Ρ ΠΈΠΏΠΎΠΏΠ»Π°Π·ΠΈΡΠ° Π²ΠΎ Π΅Π΄Π½Π° ΡΠ°ΠΌΠΈΠ»ΠΈΡΠ°
Micromastia or breast hypoplasia is described as underdevelopment of a woman's mammary tissue. We present the case of a 15-year-old girl with unilateral micromastia, with familial predisposition. Ultrasound, hormonal, dysmorphic, cardiologic, genetic examinations and testing were performed. No mutation in the whole- exome sequencing was found, nor novel mutation. Some of these cases have been reported to be related to breΓΒ°st cancer so further follow-up is mandatory. Therapy consists of surgical reconstruction of the affected breast. This is a rare condition and it requires a multidisciplinary approach.ΠΠΈΠΊΡΠΎΠΌΠ°ΡΡΠΈΡΠ° ΠΈΠ»ΠΈ Ρ
ΠΈΠΏΠΎΠΏΠ»Π°Π·ΠΈΡΠ° Π½Π° Π΄ΠΎΡΠΊΠΈ Π΅ ΠΎΠΏΠΈΡΠ°Π½Π° ΠΊΠ°ΠΊΠΎ Π½Π΅Π΄ΠΎΡΠ°Π·Π²ΠΈΠ΅Π½ΠΎΡΡ Π½Π° ΡΠΊΠΈΠ²ΠΎΡΠΎ Π½Π° Π΄ΠΎΡΠΊΠ°ΡΠ° ΠΊΠ°Ρ ΠΆΠ΅Π½ΠΈΡΠ΅. ΠΠΏΠΈΡΠ°Π²ΠΌΠ΅ ΡΠ»ΡΡΠ°Ρ Π½Π° 15-Π³ΠΎΠ΄ΠΈΡΠ½ΠΎ Π΄Π΅Π²ΠΎΡΡΠ΅ ΡΠΎ ΡΠ½ΠΈΠ»Π°ΡΠ΅ΡΠ°Π»Π½Π° ΠΌΠΈΠΊΡΠΎΠΌΠ°ΡΡΠΈΡΠ° ΡΠΎ ΡΠ°ΠΌΠΈΠ»ΠΈΡΠ°ΡΠ½Π° ΠΏΡΠ΅Π΄ΠΈΡΠΏΠΎΠ·ΠΈΡΠΈΡΠ°. ΠΠ΅Π° Π½Π°ΠΏΡΠ°Π²Π΅Π½ΠΈ Π΅Ρ
ΠΎΡΠΎΠ½ΠΎΠ³ΡΠ°ΡΡΠΊΠΈ, Ρ
ΠΎΡΠΌΠΎΠ½Π°Π»Π½ΠΈ, Π΄ΠΈΡΠΌΠΎΡΡΠΈΡΠ½ΠΈ, ΠΊΠ°ΡΠ΄ΠΈΠΎΠ»ΠΎΡΠΊΠΈ ΠΈ Π³Π΅Π½Π΅ΡΡΠΊΠΈ ΠΈΡΠΏΠΈΡΡΠ²Π°ΡΠ° ΠΈ ΡΠ΅ΡΡΠΎΠ²ΠΈ. ΠΠ΅ Π±Π΅ΡΠ΅ ΠΏΡΠΎΠ½Π°ΡΠ΄Π΅Π½Π° ΠΌΡΡΠ°ΡΠΈΡΠ° Π½Π° ΡΠ΅Π»ΠΎΠΊΡΠΏΠ½ΠΈΠΎΡ ΡΠ΅ΠΊΠ²Π΅Π½ΡΠΈΠΎΠ½ΠΈΡΠ°Π½ Π΅ΠΊΡΠΎΠΌ, Π½ΠΈΡΡ ΠΏΠ°ΠΊ Π½ΠΎΠ²Π° ΠΌΡΡΠ°ΡΠΈΡΠ°. ΠΠ΅ΠΊΠΎΠΈ ΠΎΠ΄ ΠΎΠ²ΠΈΠ΅ ΡΠ»ΡΡΠ°ΠΈ ΡΠ΅ ΠΏΡΠΈΠΊΠ°ΠΆΠ°Π½ΠΈ ΠΊΠ°ΠΊΠΎ Π΄Π° ΡΠ΅ ΠΏΠΎΠ²ΡΠ·Π°Π½ΠΈ ΡΠΎ ΠΊΠ°Π½ΡΠ΅Ρ Π½Π° Π΄ΠΎΡΠΊΠ°ΡΠ° ΠΈ Π·Π°ΡΠΎΠ° ΡΠ΅ ΠΏΠΎΡΡΠ΅Π±Π½ΠΈ ΠΏΠΎΠ½Π°ΡΠ°ΠΌΠΎΡΠ½ΠΈ Π·Π°Π΄ΠΎΠ»ΠΆΠΈΡΠ΅Π»Π½ΠΈ ΡΠ»Π΅Π΄Π΅ΡΠ°. Π’Π΅ΡΠ°ΠΏΠΈΡΠ°ΡΠ° ΡΠ΅ ΡΠΎΡΡΠΎΠΈ ΠΎΠ΄ Ρ
ΠΈΡΡΡΡΠΊΠ° ΡΠ΅ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΡΠ° Π½Π° Π°ΡΠ΅ΠΊΡΠΈΡΠ°Π½Π°ΡΠ° Π΄ΠΎΡΠΊΠ°. ΠΠ²Π° ΠΏΡΠ΅ΡΡΡΠ°Π²ΡΠ²Π° ΡΠ΅ΡΠΊΠ° ΡΠΎΡΡΠΎΡΠ±Π°, Π½ΠΎ Π±Π°ΡΠ° ΠΌΡΠ»ΡΠΈΠ΄ΠΈΡΡΠΈΠΏΠ»ΠΈΠ½Π°ΡΠ΅Π½ ΠΏΡΠΈΡΡΠ°ΠΏ
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