Call for Paper - January 2023 Edition
IJCA solicits original research papers for the January 2023 Edition. Last date of manuscript submission is December 20, 2022. Read More

Some Results on Degree of Vertices in Semitotal-Block Graph and Total-Block Graph

Print
PDF
International Journal of Computer Applications
© 2012 by IJCA Journal
Volume 50 - Number 9
Year of Publication: 2012
Authors:
Bhavanari Satyanarayana
Devanaboina Srinivasulu
Kuncham Syam Prasad
Eswaraiah Setty S.
10.5120/7799-0916

Bhavanari Satyanarayana, Devanaboina Srinivasulu, Kuncham Syam Prasad and Eswaraiah Setty S.. Article: Some Results on Degree of Vertices in Semitotal-Block Graph and Total-Block Graph. International Journal of Computer Applications 50(9):19-22, July 2012. Full text available. BibTeX

@article{key:article,
	author = {Bhavanari Satyanarayana and Devanaboina Srinivasulu and Kuncham Syam Prasad and Eswaraiah Setty S.},
	title = {Article: Some Results on Degree of Vertices in Semitotal-Block Graph and Total-Block Graph},
	journal = {International Journal of Computer Applications},
	year = {2012},
	volume = {50},
	number = {9},
	pages = {19-22},
	month = {July},
	note = {Full text available}
}

Abstract

We considersemitotal-block graph, total-block graph of a graph G (respectively, denoted as Tb(G), TB(G)). We prove that the number of edges in a semitotal-block graph of a given graph G is equal to |E(G)| + |V(B1)| + |V(B2)| + … + |V(Bm)|, where B1, B2, …, Bm are the blocks of G. Further, we obtain that TB(G) is the ring sum of Tb(G) and the block graph B(G). We introduce the concept "vertex-block graph (denoted by Bv(G) of G)", andwe prove thatTb(G) is the ring sum of G and Bv(G). We also present some related fundamental results along with illustrations.

References

  • Arumugam S. and Ramachandran S. "Invitation to Graph Theory", Scitech Publications (India) Pvt. Ltd, Chennai, (2001).
  • Bondy J. A. and Murty U. S. R. "Graph Theory with Applications", The Macmillan Press Ltd, (1976).
  • Harary F. "Graph Theory", Addison-Wesley Publishing Company, USA (1972).
  • Kulli V. R. "Minimally Non outer planar Graphs: A survey", (in the Book: "Recent Studies in Graph theory" ed: V. R. Kulli), Vishwa International Publication, (1989) 177-189.
  • NarsingDeo "Graph Theory with Applications to Engineering and Computer Science", Prentice Hall of India Pvt. Ltd, New Delhi (1997).
  • SatyanarayanaBh. and Syam Prasad K. "An Isomorphism Theorem on Directed Hypercubes of Dimension n", Indian J. Pure & Appl. Math 34 (10) (2003) 1453-1457.
  • SatyanarayanBh. , and Syam Prasad K. "Discrete Mathematics and Graph Theory", Prentice Hall of India, New Delhi, 2009. ISSN:978-81-203-3842-5.
  • SatyanarayanaBh. , Syam Prasad K. ,and Nagaraju D. "Prime Graph of a Ring", Journal of Combinatorics, Information and System Sciences, Vol. 35, 1-12, (2010).
  • SatyanarayanaBh. ,Syam Prasad K. , and Srinivas K. B. 'Graph of a Nearring with respect to an Ideal', Communications in Algebra (USA) Taylor & Francis (2010), 38 (5), 1957–1967.
  • Syam Prasad K. and SatyanarayanaBh. "Finite Dimension in N-Groups and Fuzzy Ideals of Gamma Nearrings", VDM Verlag, (Germany), 2011. ISBN: 978-3-639-36838-3.