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Line Graphs and Quasi-Total Graphs
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 105 - Number 3 |
| Year of Publication: 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
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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