BibTex RIS Kaynak Göster
Yıl 2017, Cilt: 7 Sayı: 1, 173 - 179, 01.06.2017

Öz

Kaynakça

  • Beck, (1956), Coloring of Commutative Ring, J. Algebra, 116 (1988), 208-226.
  • Bondy,J.A. and Murty,U.S.R., (1976), Graph Theory with Applications, The Macmillan Press Ltd.
  • Harary,F., (1972), Graph Theory, Addison-Wesley Publishing Company, USA.
  • Narsing Deo, (1997), Graph Theory with Applications to Engineering and Computer Science, Prentice Hall of India Pvt. Ltd, New Delhi.
  • Armugam,S. and Ramachandran,S., (2001), Invitation to Graph Theory , Scitech Publications (India) Pvt. Ltd, Chennai.
  • Kulli,V.R., (1989), Minimally Non outerplanar Graphs: A survey, (in the Book: Recent Studies in Graph theory ed: V. R. Kulli) , Vishwa International Publication, pp.177-189.
  • Satyanarayana,Bh. and Syam Prasad,K., (2003), An Isomorphism Theorem on Directed Hypercubes of Dimension n, Indian J. Pure and Appl. Math, 34(10), pp.1453-1457.
  • Satyanarayana,Bh. and Syam Prasad,K., (2009), Discrete Mathematics and Graph Theory, Prentice Hall India Pvt. Ltd., New Delhi, ISBN 978-81-203-3842-5.
  • Satyanarayana,Bh. and Syam Prasad,K., (2014), Discrete Mathematics and Graph Theory, Prentice Hall India Pvt. Ltd., New Delhi, (Second Edition), ISBN 978-81-203-4948-3.
  • Satyanarayana,Bh. and Syam Prasad,K., (2013), Nearrings, Fuzzy Ideals and Graph Theory CRC Press (Taylor and Francis Group, London, New York), ISBN 13: 9781439873106.
  • Satyanarayana Bh., Syam Prasad,K., and Nagaraju,D., (2010), Prime Graph of a Ring, J. Combina- torics, Informations and System Sciences, (35), pp.27-42.
  • Satyanarayana,Bh., Srinivasulu,D., and Syam Prasad,K., (2012), Some Results on Degree of Vertices in Semitotal Block Graph and Total Block Graph, International Journal of Computer Applications (0975 - 8887), Vol.50, No.9, pp.19-22.
  • Satyanarayana,Bh., Srinivasulu,D., and Syam Prasad,K., (2014), Line Graphs and Quasi-Total Block Graphs, International Journal of Computer Applications (0975 - 8887) Vol.105, No.3, pp.12-16.

A NOTE ON LINE GRAPHS

Yıl 2017, Cilt: 7 Sayı: 1, 173 - 179, 01.06.2017

Öz

The line graph and 1-quasitotal graph are well-known concepts in graph theory. In Satyanarayana, Srinivasulu, and Syam Prasad [13], it is proved that if a graph G consists of exactly m connected components Gi 1 ≤ i ≤ m then L G = L G1 and L G1 is the ring sum of L G2 ,..., L Gm where L G denotes the line graph of G. In [13], the authors also introduced the concept 1-quasitotal graph and obtained that Q1 G is the ring sum of G and L G where Q1 G denotes 1-quasitotal graph of a given graph G. In this note, we consider zero divisor graph of a nite associate ring R and we will prove that the line graph of Kn-1 contains the complete graph on n vertices where n is the number of elements in the ring R.

Kaynakça

  • Beck, (1956), Coloring of Commutative Ring, J. Algebra, 116 (1988), 208-226.
  • Bondy,J.A. and Murty,U.S.R., (1976), Graph Theory with Applications, The Macmillan Press Ltd.
  • Harary,F., (1972), Graph Theory, Addison-Wesley Publishing Company, USA.
  • Narsing Deo, (1997), Graph Theory with Applications to Engineering and Computer Science, Prentice Hall of India Pvt. Ltd, New Delhi.
  • Armugam,S. and Ramachandran,S., (2001), Invitation to Graph Theory , Scitech Publications (India) Pvt. Ltd, Chennai.
  • Kulli,V.R., (1989), Minimally Non outerplanar Graphs: A survey, (in the Book: Recent Studies in Graph theory ed: V. R. Kulli) , Vishwa International Publication, pp.177-189.
  • Satyanarayana,Bh. and Syam Prasad,K., (2003), An Isomorphism Theorem on Directed Hypercubes of Dimension n, Indian J. Pure and Appl. Math, 34(10), pp.1453-1457.
  • Satyanarayana,Bh. and Syam Prasad,K., (2009), Discrete Mathematics and Graph Theory, Prentice Hall India Pvt. Ltd., New Delhi, ISBN 978-81-203-3842-5.
  • Satyanarayana,Bh. and Syam Prasad,K., (2014), Discrete Mathematics and Graph Theory, Prentice Hall India Pvt. Ltd., New Delhi, (Second Edition), ISBN 978-81-203-4948-3.
  • Satyanarayana,Bh. and Syam Prasad,K., (2013), Nearrings, Fuzzy Ideals and Graph Theory CRC Press (Taylor and Francis Group, London, New York), ISBN 13: 9781439873106.
  • Satyanarayana Bh., Syam Prasad,K., and Nagaraju,D., (2010), Prime Graph of a Ring, J. Combina- torics, Informations and System Sciences, (35), pp.27-42.
  • Satyanarayana,Bh., Srinivasulu,D., and Syam Prasad,K., (2012), Some Results on Degree of Vertices in Semitotal Block Graph and Total Block Graph, International Journal of Computer Applications (0975 - 8887), Vol.50, No.9, pp.19-22.
  • Satyanarayana,Bh., Srinivasulu,D., and Syam Prasad,K., (2014), Line Graphs and Quasi-Total Block Graphs, International Journal of Computer Applications (0975 - 8887) Vol.105, No.3, pp.12-16.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

S. Bhavanari Bu kişi benim

S. Devanaboina Bu kişi benim

S. P. Kuncham Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 7 Sayı: 1

Kaynak Göster