Research Article
Some Results on Degree of Vertices in Semitotal-Block Graph and Total-Block Graph
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 50 - Issue 9 |
| Published: July 2012 |
| Authors: Bhavanari Satyanarayana, Devanaboina Srinivasulu, Kuncham Syam Prasad, Eswaraiah Setty S. |
10.5120/7799-0916
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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
@article{ 10.5120/7799-0916,
author = { Bhavanari Satyanarayana,Devanaboina Srinivasulu,Kuncham Syam Prasad,Eswaraiah Setty S. },
title = { 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 },
doi = { 10.5120/7799-0916 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2012
%A Bhavanari Satyanarayana
%A Devanaboina Srinivasulu
%A Kuncham Syam Prasad
%A Eswaraiah Setty S.
%T Some Results on Degree of Vertices in Semitotal-Block Graph and Total-Block Graph%T
%J International Journal of Computer Applications
%V 50
%N 9
%P 19-22
%R 10.5120/7799-0916
%I Foundation of Computer Science (FCS), NY, USA
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.
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