The week's pick
Random Articles
Reseach Article
Some Results on Degree of Vertices in Semitotal-Block Graph and Total-Block Graph
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| 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, Eswaraiah Setty S. . Some Results on Degree of Vertices in Semitotal-Block Graph and Total-Block Graph. International Journal of Computer Applications. 50, 9 ( July 2012), 19-22. DOI=10.5120/7799-0916
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.
Index Terms
Keywords