BibTex RIS Cite
Year 2017, Volume: 7 Issue: 1, 173 - 179, 01.06.2017

Abstract

References

  • 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

Year 2017, Volume: 7 Issue: 1, 173 - 179, 01.06.2017

Abstract

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.

References

  • 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.
There are 13 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

S. Bhavanari This is me

S. Devanaboina This is me

S. P. Kuncham This is me

Publication Date June 1, 2017
Published in Issue Year 2017 Volume: 7 Issue: 1

Cite