Graceful Labeling of Generalized Theta graphs

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Abstract

A generalized theta graph consisting of n internal disjoint paths, in which each path contains m vertices and path end vertices are merged with the vertices \({\hbox {v}}_{1}\) and \({\hbox {v}}_{2}\) respectively. This graph is denoted as \(\theta ({\hbox {nP}}_{m})\). We proved \(\theta ({\hbox {nP}}_{m})\) is graceful for \({\hbox {m}} = 2{\hbox {j}} + 1\) and \({\hbox {j}} = 1, 2, \dots , {\hbox {n}}\).

Keywords

Graceful labeling Theta graph General theta graph 

Mathematics Subject Classification

05C78 

References

  1. 1.
    Rosa A (1967) On certain valuations of the vertices of a graph. In: International symposium on theory of graphs, Rome, July 1966, Gordon and Breach, NY and Dunod, Paris, pp 349–355Google Scholar
  2. 2.
    Gallian JA (2013) A dynamic survey of graph labeling. Electron J Comb 16:1–432Google Scholar

Copyright information

© The National Academy of Sciences, India 2018

Authors and Affiliations

  1. 1.SASTRA Deemed UniversityThanjavurIndia
  2. 2.NITTiruchirappalliIndia

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