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Some New Classes of Open Distance-Pattern Uniform Graphs
Author
Source
International Journal of Combinatorics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-07-24
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
Given an arbitrary nonempty subset M of vertices in a graph G=(V,E), each vertex u in G is associated with the set fMo(u)={d(u,v):v∈M,u≠v} and called its open M-distance-pattern.
The graph G is called open distance-pattern uniform (odpu-) graph if there exists a subset M of V(G) such that fMo(u)=fMo(v) for all u,v∈V(G), and M is called an open distance-pattern uniform (odpu-) set of G.
The minimum cardinality of an odpu-set in G, if it exists, is called the odpu-number of G and is denoted by od(G).
Given some property P, we establish characterization of odpu-graph with property P.
In this paper, we characterize odpu-chordal graphs, and thereby characterize interval graphs, split graphs, strongly chordal graphs, maximal outerplanar graphs, and ptolemaic graphs that are odpu-graphs.
We also characterize odpu-self-complementary graphs, odpu-distance-hereditary graphs, and odpu-cographs.
We prove that the odpu-number of cographs is even and establish that any graph G can be embedded into a self-complementary odpu-graph H, such that G and G¯ are induced subgraphs of H.
We also prove that the odpu-number of a maximal outerplanar graph is either 2 or 5.
American Psychological Association (APA)
Jose, Bibin K.. 2013. Some New Classes of Open Distance-Pattern Uniform Graphs. International Journal of Combinatorics،Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-504382
Modern Language Association (MLA)
Jose, Bibin K.. Some New Classes of Open Distance-Pattern Uniform Graphs. International Journal of Combinatorics No. 2013 (2013), pp.1-7.
https://search.emarefa.net/detail/BIM-504382
American Medical Association (AMA)
Jose, Bibin K.. Some New Classes of Open Distance-Pattern Uniform Graphs. International Journal of Combinatorics. 2013. Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-504382
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-504382