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Reseach Article

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

by Bhavanari Satyanarayana, Devanaboina Srinivasulu, Kuncham Syam Prasad, Eswaraiah Setty S.
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

@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 },
issue_date = { July 2012 },
volume = { 50 },
number = { 9 },
month = { July },
year = { 2012 },
issn = { 0975-8887 },
pages = { 19-22 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume50/number9/7799-0916/ },
doi = { 10.5120/7799-0916 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:47:50.476164+05:30
%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
%J International Journal of Computer Applications
%@ 0975-8887
%V 50
%N 9
%P 19-22
%D 2012
%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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Index Terms

Computer Science
Information Sciences

Keywords

Degree of vertex Semitotal-block graph Total-block graph