• Bibin K. Jose

Given an arbitrary nonempty subset A of vertices in a (p, q)-graph G = (V, E), each vertex u in G is associated with the set fo (u) = {d(u, v) : v ∈ A, u /= v}, where d(x, y) denotes the usual distance between the vertices x and y in G, called its open A-distance pattern. G is called an open distance-pattern uniform (or, in short, odpu)-graph if there exists a nonempty subset A ⊆ V (G) such that fo (u) is independent of the choice of u ∈ V (G), where the set-valued function (or, set-valuation) fo is called the open distance pattern uniform (or, an odpu-) labeling of G and A is called an odpu-set of G. The minimum cardinality of an odpu-set in G, if it exists, is the odpu-number ς(G) of G. Given any 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 and ptolemaic graphs that are odpu-graphs. We also characterize odpu-distance hereditary graphs.

Open distance-pattern uniform graphs, Open distance- pattern uniform (odpu-) set, Odpu-number, odpu-chordal graphs, odpu-interval graphs, odpu-split graphs, odpu-strongly chordal graphs, odpu-ptolemaic graphs, odpu-distance hereditary graphs.

"A CHARACTERIZATION OF OPEN DISTANCE PATTERN UNIFORM CHORDAL GRAPHS AND DISTANCE HEREDITARY GRAPHS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.4, Issue 8, page no.618-624, August-2017, Available :http://www.jetir.org/papers/JETIR1708095.pdf

"A CHARACTERIZATION OF OPEN DISTANCE PATTERN UNIFORM CHORDAL GRAPHS AND DISTANCE HEREDITARY GRAPHS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.4, Issue 8, page no. pp618-624, August-2017, Available at : http://www.jetir.org/papers/JETIR1708095.pdf