EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE

İbrahim Günaltı

Araştırma Makalesi

EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE

Yıl 2015, Cilt: 3 Sayı: 1, 121 - 125, 01.04.2015

İbrahim Günaltı

Öz

Let S = (P;L) be a non-trivial regular nite linear space with v points, v + k lines, k 3: We show that if S contains at least 􀀀k 2 lines of size b(p) 􀀀 2 and one line size b(p) for some point p, then S is embeddable in a unique projective plane of order b(p) 􀀀 1 and 􀀀 s is a complete graph of order k ; where b(p) 4 for some point p:

Anahtar Kelimeler

linear space, projective plane, complete graph

Kaynakça

[1] Batten , L.M. and Beutelspacher, A. ; Combinatorics of points and lines, Cambridge Univer- sity Press, 1993.
[2] Batten, L.M. ; Embedding pseudo-complements in nite projective planes, Ars Combin. 24 (1987), 129-132.
[3] Bose , R.C. and Shrikhande, S.S. ; Embedding the complement of a oval in a projective plane of even order, Discrete Math. 6 (1973), 305-312.
[4] Bruck, R. H. ; Existence problems for classes of nite projective planes, Lectures delivered to the Canadian Math. Congress, Sask., Aug.1963.
[5] De Brujin N.G and Erdos, P. ; On a combinatorial problem, Nederl Akad.Wetemsch. proc. Sect. Sci. 51 (1948), 1277 - 1279.
[6] De Witte, P. ;The exceptional case in a Theorem of Bose and Shrikhande, J. Austral.Math. soc. 24 (Series A) (1977), 64-78.
[7] Dickey, L. J. ; Embedding the complement of a unital in a projective plane, Atti del convegno di Geometria Combinatoria e sue Applicazioni, Perugia, 1971, pp. 199-203.
[8] Gunaltl, _I. and Olgun, S. ; On the embedding some linear spaces in nite projective planes. J.geom. 68 (2000) 96-99.
[9] Gunaltl, _I. , Anapa, P. and Olgun, S. ; On the embedding of complements of some hyperbolic planes. Ars Combin. 80 (2006), pp. 205-214.
[10] Hall, M. ; Projective planes, Trans. Amer. Math. Soc. 54 (1943) 229-277.
[11] Kaya, R. and Ozcan, E. ; On the construction of B-L planes from projective planes, Rendiconti del Seminario Matematico Di Bresciot (1984), pp. 427-434.
[12] Mullin, R.C. and Vanstone, S.A. ; Embedding the pseudo-complements of a quadrilateral in a nite projective plane, Ann.New York Acad.Sci.319, 405-412.
[13] Totten, J. ; Embedding the complement of two lines in a nite projective plane, J.Austral.Math.Soc. 22 (Series A) (1976), 27-34.

Yıl 2015, Cilt: 3 Sayı: 1, 121 - 125, 01.04.2015

İbrahim Günaltı

Öz

Kaynakça

[1] Batten , L.M. and Beutelspacher, A. ; Combinatorics of points and lines, Cambridge Univer- sity Press, 1993.
[2] Batten, L.M. ; Embedding pseudo-complements in nite projective planes, Ars Combin. 24 (1987), 129-132.
[3] Bose , R.C. and Shrikhande, S.S. ; Embedding the complement of a oval in a projective plane of even order, Discrete Math. 6 (1973), 305-312.
[4] Bruck, R. H. ; Existence problems for classes of nite projective planes, Lectures delivered to the Canadian Math. Congress, Sask., Aug.1963.
[5] De Brujin N.G and Erdos, P. ; On a combinatorial problem, Nederl Akad.Wetemsch. proc. Sect. Sci. 51 (1948), 1277 - 1279.
[6] De Witte, P. ;The exceptional case in a Theorem of Bose and Shrikhande, J. Austral.Math. soc. 24 (Series A) (1977), 64-78.
[7] Dickey, L. J. ; Embedding the complement of a unital in a projective plane, Atti del convegno di Geometria Combinatoria e sue Applicazioni, Perugia, 1971, pp. 199-203.
[8] Gunaltl, _I. and Olgun, S. ; On the embedding some linear spaces in nite projective planes. J.geom. 68 (2000) 96-99.
[9] Gunaltl, _I. , Anapa, P. and Olgun, S. ; On the embedding of complements of some hyperbolic planes. Ars Combin. 80 (2006), pp. 205-214.
[10] Hall, M. ; Projective planes, Trans. Amer. Math. Soc. 54 (1943) 229-277.
[11] Kaya, R. and Ozcan, E. ; On the construction of B-L planes from projective planes, Rendiconti del Seminario Matematico Di Bresciot (1984), pp. 427-434.
[12] Mullin, R.C. and Vanstone, S.A. ; Embedding the pseudo-complements of a quadrilateral in a nite projective plane, Ann.New York Acad.Sci.319, 405-412.
[13] Totten, J. ; Embedding the complement of two lines in a nite projective plane, J.Austral.Math.Soc. 22 (Series A) (1976), 27-34.

Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Mühendislik
Bölüm	Articles
Yazarlar	İbrahim Günaltı
Yayımlanma Tarihi	1 Nisan 2015
Gönderilme Tarihi	10 Temmuz 2014
Yayımlandığı Sayı	Yıl 2015 Cilt: 3 Sayı: 1

Kaynak Göster

APA	Günaltı, İ. (2015). EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE. Konuralp Journal of Mathematics, 3(1), 121-125.
AMA	Günaltı İ. EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE. Konuralp J. Math. Nisan 2015;3(1):121-125.
Chicago	Günaltı, İbrahim. “EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE”. Konuralp Journal of Mathematics 3, sy. 1 (Nisan 2015): 121-25.
EndNote	Günaltı İ (01 Nisan 2015) EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE. Konuralp Journal of Mathematics 3 1 121–125.
IEEE	İ. Günaltı, “EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE”, Konuralp J. Math., c. 3, sy. 1, ss. 121–125, 2015.
ISNAD	Günaltı, İbrahim. “EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE”. Konuralp Journal of Mathematics 3/1 (Nisan 2015), 121-125.
JAMA	Günaltı İ. EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE. Konuralp J. Math. 2015;3:121–125.
MLA	Günaltı, İbrahim. “EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE”. Konuralp Journal of Mathematics, c. 3, sy. 1, 2015, ss. 121-5.
Vancouver	Günaltı İ. EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE. Konuralp J. Math. 2015;3(1):121-5.

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