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1
Content available On generalized Pell numbers and their graph representations
100%
Włoch I.
Commentationes Mathematicae
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2008
|
tom 48
|
nr 2
EN
In this paper we give a generalization of the Pell numbers and the Pell-Lucas numbers and next we apply this concept for their graph representations. We shall show that the generalized Pell numbers and the Pell-Lucas numbers are equal to the total number of k-independent sets in special graphs.
2
Content available remote On kernels by monochromatic paths in the corona of digraphs
100%
Włoch I.
Open Mathematics
|
2008
|
tom 6
|
nr 4
537-542
EN
In this paper we derive necessary and sufficient conditions for the existence of kernels by monochromatic paths in the corona of digraphs. Using these results, we are able to prove the main result of this paper which provides necessary and sufficient conditions for the corona of digraphs to be monochromatic kernel-perfect. Moreover we calculate the total numbers of kernels by monochromatic paths, independent by monochromatic paths sets and dominating by monochromatic paths sets in this digraphs product.
3
Content available A note on (k,l)-kernels in B-products of graphs
100%
Włoch I.
Discussiones Mathematicae Graph Theory
|
1996
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tom 16
|
nr 2
119-122
EN
B-products of graphs and their generalizations were introduced in [4]. We determined the parameters k, l of (k,l)-kernels in generalized B-products of graphs. These results are generalizations of theorems from [2].
4
Content available On Pell and Pell−Lucas Hybrid Numbers
63%
Szynal-Liana A. , Włoch I.
Commentationes Mathematicae
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2018
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tom 58
|
nr 1-2
EN
In this paper we introduce the Pell and Pell−Lucas hybrid numbers as special kinds of hybrid numbers. We describe some properties of Pell hybrid numbers and Pell−Lucas hybrid numbers among other we give the Binet formula, the character and the generating function for these numbers.
5
Content available On generalized Mersenne hybrid numbers
63%
Szynal-Liana A. , Włoch I.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
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2020
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tom 74
|
nr 1
EN
The hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper we consider  a special kind of hybrid numbers, namely the Mersenne hybrid numbers and we give some of their properties.
6
Content available remote Fibonacci and Telephone Numbers in Extremal Trees
63%
Bednarz U. , Włoch I.
Discussiones Mathematicae Graph Theory
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2017
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tom 38
|
nr 1
121-133
EN
In this paper we shall show applications of the Fibonacci numbers in edge-coloured trees. In particular we determine the successive extremal graphs in the class of trees with respect to the number of (A, 2B)-edge colourings. We show connections between these numbers and Fibonacci numbers as well as the telephone numbers.
7
Content available On F(p, n) - Fibonacci quaternions
63%
Szynal-Liana A. , Włoch I.
Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations
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2018
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tom 68
|
nr 1
PL
https://doi.org/10.26485/0459-6854/2018/68.1/9 W pracy wprowadzamy i badamy jednoparametrowe uogólnienie kwaternionów Fibonacciego. Podajemy własności kwaternionów F(p, n) Fibonacciego, a także uogólnienia klasycznych wyników dla kwaternionów Fibonacciego.
EN
https://doi.org/10.26485/0459-6854/2018/68.1/9 In this paper we introduce and study a special one-parameter generalization of Fibonacci quaternions. We investigate their properties and we give generalizations of some classical results for Fibonacci quaternions.
8
Content available Note about sequences of extrema \((A,2B)\)-edge coloured trees
63%
Bednarz U. , Włoch I.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2017
|
tom 71
|
nr 2
EN
In this paper we determine successive extremal trees with respect to the number of all \((A,2B)\)-edge colourings.
9
Content available On (2-d)-kernels in the cartesian product of graphs
63%
Bednarz P. , Włoch I.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2016
|
tom 70
|
nr 2
EN
In this paper we study the problem of the existence of (2-d)-kernels in the cartesian product of graphs. We give sufficient conditions for the existence of (2-d)-kernels in the cartesian product and also we consider the number of (2-d)-kernels.
10
Content available On some kind of numbers of the Fibonacci type and their applications for bicomplex numbers
51%
Liana M. , Szynal-Liana A. , Włoch I.
Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations
|
2019
|
tom 69
|
nr 1
129-138
PL
W pracy pokazane zostało zastosowanie pewnego rodzaju liczb typu Fibonacciego w teorii liczb dwuzespolonych.
EN
In this paper we introduce a special kind of numbers of the Fibonacci type and we show some their applications in the theory of bicomplex numbers.
11
Content available On (k,l)-kernels in D-join of digraphs
51%
Szumny W. , Włoch A. , Włoch I.
Discussiones Mathematicae Graph Theory
|
2007
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tom 27
|
nr 3
457-470
EN
In [5] the necessary and sufficient conditions for the existence of (k,l)-kernels in a D-join of digraphs were given if the digraph D is without circuits of length less than k. In this paper we generalize these results for an arbitrary digraph D. Moreover, we give the total number of (k,l)-kernels, k-independent sets and l-dominating sets in a D-join of digraphs.
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