Research Article
Line Graphs and Quasi-Total Graphs
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 105 - Issue 3 |
| Published: November 2014 |
| Authors: Bhavanari Satyanarayana, Devanaboina Srinivasulu, Kuncham Syam Prasad |
10.5120/18356-9483
|
Bhavanari Satyanarayana, Devanaboina Srinivasulu, Kuncham Syam Prasad . Line Graphs and Quasi-Total Graphs. International Journal of Computer Applications. 105, 3 (November 2014), 12-16. DOI=10.5120/18356-9483
@article{ 10.5120/18356-9483,
author = { Bhavanari Satyanarayana,Devanaboina Srinivasulu,Kuncham Syam Prasad },
title = { Line Graphs and Quasi-Total Graphs },
journal = { International Journal of Computer Applications },
year = { 2014 },
volume = { 105 },
number = { 3 },
pages = { 12-16 },
doi = { 10.5120/18356-9483 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2014
%A Bhavanari Satyanarayana
%A Devanaboina Srinivasulu
%A Kuncham Syam Prasad
%T Line Graphs and Quasi-Total Graphs%T
%J International Journal of Computer Applications
%V 105
%N 3
%P 12-16
%R 10.5120/18356-9483
%I Foundation of Computer Science (FCS), NY, USA
Abstract
The line graph, 1-quasitotal graph and 2-quasitotal graph are well-known. It is proved that if G is a graph consist of exactly m connected components Gi, 1 ? i ? m, then L(G) = L(G1) Å L(G2) Å … Å L(Gm) where L(G) denotes the line graph of G, and 'Å' denotes the ring sum operation on graphs. The number of connected components in G is equal to the number of connected components in L(G) and also if G is a cycle of length n, then L(G) is also a cycle of length n. The concept of 1-quasitotal graph is introduced and obtained that Q1(G) = G Å L(G) where Q1(G) denotes 1-quasitotal graph of a given graph G. It is also proved that for a 2-quasitotal graph of G, the two conditions (i) |E(G)|= 1; and (ii) Q2(G) contains unique triangle are equivalent.
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