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On Partitional and Other Related Graphs

On Partitional and Other Related Graphs The partitional graphs, which are a subclass of the sequential graphs, were recently introduced by Ichishima and Oshima (Math Comput Sci 3:39–45, 2010), and the cartesian product of a partitional graph and K 2 was shown to be partitional, sequential, harmonious and felicitous. In this paper, we present some necessary conditions for a graph to be partitional. By means of these, we study the partitional properties of certain classes of graphs. In particular, we completely characterize the classes of the graphs B m and K m,2 × Q n that are partitional. We also establish the relationships between partitional graphs and graphs with strong α-valuations as well as strongly felicitous graphs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematics in Computer Science Springer Journals

On Partitional and Other Related Graphs

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References (15)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Basel AG
Subject
Mathematics; Mathematics, general; Computer Science, general
ISSN
1661-8270
eISSN
1661-8289
DOI
10.1007/s11786-011-0082-5
Publisher site
See Article on Publisher Site

Abstract

The partitional graphs, which are a subclass of the sequential graphs, were recently introduced by Ichishima and Oshima (Math Comput Sci 3:39–45, 2010), and the cartesian product of a partitional graph and K 2 was shown to be partitional, sequential, harmonious and felicitous. In this paper, we present some necessary conditions for a graph to be partitional. By means of these, we study the partitional properties of certain classes of graphs. In particular, we completely characterize the classes of the graphs B m and K m,2 × Q n that are partitional. We also establish the relationships between partitional graphs and graphs with strong α-valuations as well as strongly felicitous graphs.

Journal

Mathematics in Computer ScienceSpringer Journals

Published: Sep 24, 2011

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