Plik:GraphGoddnumbers.png - Historia wersji

AndrzejSalwicki o 11:47, 10 sie 2026

2026-08-10T11:47:01Z

2026-08-10T11:43:44Z

2026-08-10T11:42:22Z

2026-08-10T11:41:28Z

2026-08-10T11:38:20Z

2026-08-10T11:37:40Z

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2026-08-10T11:21:35Z

← poprzednia wersja		Wersja z 11:47, 10 sie 2026
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	A pair <math>\langle n,m\rangle </math> of odd numbers is an edge iff <math>n</math> is indivisible by 3 and there exists the natural number <math>i>0</math> such that <math>\color{blue} m=\frac{n\cdot 2^{2i-(n \mod 3)-1}-1}{3}</math>		A pair <math>\langle n,m\rangle </math> of odd numbers is an edge iff <math>n</math> is indivisible by 3 and there exists the natural number <math>i>0</math> such that <math>\color{blue} m=\frac{n\cdot 2^{2i-(n \mod 3)-1}-1}{3}</math>
		+	=== Lemma ===
		+	The graph <math>G</math> is a tree iff the graph <math>HC</math> is a tree.
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← poprzednia wersja		Wersja z 11:43, 10 sie 2026
Linia 5:		Linia 5:

	A pair <math>\langle n,m\rangle </math> of odd numbers is an edge iff <math>n</math> is indivisible by 3 and there exists the natural number <math>i>0</math> such that <math>\color{blue} m=\frac{n\cdot 2^{2i-(n \mod 3)-1}-1}{3}</math>		A pair <math>\langle n,m\rangle </math> of odd numbers is an edge iff <math>n</math> is indivisible by 3 and there exists the natural number <math>i>0</math> such that <math>\color{blue} m=\frac{n\cdot 2^{2i-(n \mod 3)-1}-1}{3}</math>
		+	-----

← poprzednia wersja		Wersja z 11:42, 10 sie 2026
Linia 4:		Linia 4:
	The set of all odd natural numbers constitutes the set <math>V</math>.<br />		The set of all odd natural numbers constitutes the set <math>V</math>.<br />

−	A pair <math>\langle n,m\rangle </math> of odd numbers is an edge iff <math>n</math> is indivisible by 3 and there exists the natural number <math>i>0</math> such that <math>\color{blue} m=\frac{n\cdot 2^{2i-n \mod 3-1}-1}{3}</math>	+	A pair <math>\langle n,m\rangle </math> of odd numbers is an edge iff <math>n</math> is indivisible by 3 and there exists the natural number <math>i>0</math> such that <math>\color{blue} m=\frac{n\cdot 2^{2i-(n \mod 3)-1}-1}{3}</math>

← poprzednia wersja		Wersja z 11:41, 10 sie 2026
Linia 4:		Linia 4:
	The set of all odd natural numbers constitutes the set <math>V</math>.<br />		The set of all odd natural numbers constitutes the set <math>V</math>.<br />

−	A pair <math>\langle n,m\rangle </math> of odd numbers is an edge iff <math>n</math> is indivisible by 3 and there exists the natural number <math>i>0</math> such that <math>\color{blue} m=\frac{n\cdot 2^i-1}{3}</math>	+	A pair <math>\langle n,m\rangle </math> of odd numbers is an edge iff <math>n</math> is indivisible by 3 and there exists the natural number <math>i>0</math> such that <math>\color{blue} m=\frac{n\cdot 2^{2i-n \mod 3-1}-1}{3}</math>

← poprzednia wersja		Wersja z 11:38, 10 sie 2026
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−	=== ~~Definiction~~ of the graph G ===	+	=== Definition of the graph G ===
	<math> \color{blue}G=\langle V,E \rangle </math><br />		<math> \color{blue}G=\langle V,E \rangle </math><br />

← poprzednia wersja		Wersja z 11:37, 10 sie 2026
Linia 4:		Linia 4:
	The set of all odd natural numbers constitutes the set <math>V</math>.<br />		The set of all odd natural numbers constitutes the set <math>V</math>.<br />

−	A pair <math>\langle n,m\rangle </math> of odd numbers is an edge iff <math>n</math> is indivisible by 3 and there exists the natural number <math>i>0</math> such that <math>m=\frac{n\cdot 2^i-1}{3}</math>	+	A pair <math>\langle n,m\rangle </math> of odd numbers is an edge iff <math>n</math> is indivisible by 3 and there exists the natural number <math>i>0</math> such that <math>\color{blue} m=\frac{n\cdot 2^i-1}{3}</math>

@@ Linia 1: / Linia 1: @@
 === Definiction of the graph  G  ===
-<math> \color{blue}G=\langle V,E \rangle \color{black}</math><br />
+<math> \color{blue}G=\langle V,E \rangle </math><br />
 The set of all odd natural numbers constitutes the set <math>V</math>.<br />
 A pair <math>\langle  n,m\rangle </math> of odd numbers is an edge iff <math>n</math> is indivisible by 3 and  there exists the natural number <math>i>0</math> such that <math>m=\frac{n\cdot 2^i-1}{3}</math>

← poprzednia wersja		Wersja z 11:21, 10 sie 2026
Linia 4:		Linia 4:
	The set of all odd natural numbers constitutes the set <math>V</math>.<br />		The set of all odd natural numbers constitutes the set <math>V</math>.<br />

−	A pair <math> n,m </math> of odd numbers is an edge iff <math>n</math> is indivisible by 3 and <math>m=\frac{n\cdot 2^i-1}{3}</math>	+	A pair <math>\langle n,m\rangle </math> of odd numbers is an edge iff <math>n</math> is indivisible by 3 and there exists the natural number <math>i>0</math> such that <math>m=\frac{n\cdot 2^i-1}{3}</math>