Line Graphs and Quasi-total Graphs

Bhavanari, Satyanarayana and Srinivasulu, Devanaboina and Kuncham, Syam Prasad (2014) Line Graphs and Quasi-total Graphs. International Journal of Computer Applications, 105 (3). pp. 12-16. ISSN 0975 – 8887

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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)  L(G2)  …  L(Gm) where L(G) denotes the line graph of G, and „‟ 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 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

Item Type: Article
Uncontrolled Keywords: Line graph, quasi total graph, connected component
Subjects: Engineering > MIT Manipal > Mathematics
Depositing User: MIT Library
Date Deposited: 14 Jan 2015 09:02
Last Modified: 14 Jan 2015 09:02
URI: http://eprints.manipal.edu/id/eprint/141585

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