Some New Classes of Open Distance-Pattern Uniform Graphs. (24th July 2013)

• Record Type: Journal Article
• Authors: Jose, Bibin K.
• Other Names: Mansour Toufik Academic Editor.
• Is Part Of: International journal of combinatorics. Volume 2013(2013)
• Publication Date: 2013-07-24
• Subjects: Combinatorial analysis -- Periodicals; Combinatorial analysis; Periodicals; Electronic journals; 511.605
• DOI: 10.1155/2013/863439
• Languages: English
• ISSNs: 1687-9163

Abstract

Abstract : Given an arbitrary nonempty subsetM of vertices in a graphG = ( V, E ), each vertexu inG is associated with the setf M o ( u ) = { d ( u, v ) : v ∈ M, u ≠ v } and called its openM -distance-pattern. The graphG is called open distance-pattern uniform (odpu-) graph if there exists a subsetM ofV ( G ) such thatf M o ( u ) = f M o ( v ) for allu, v ∈ V ( G ), andM is called an open distance-pattern uniform (odpu-) set ofG . The minimum cardinality of an odpu-set inG, if it exists, is called the odpu-number ofG and is denoted byod ( G ) . Given some propertyP, we establish characterization of odpu-graph with propertyP . 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 graphG can be embedded into a self-complementary odpu-graphH, such thatG andG ¯ are induced subgraphs ofH . We also prove that the odpu-number of a maximal outerplanar graph is either2 or5 .