IJPAM: Volume 87, No. 5 (2013)

DETOUR DISTANCE PATTERN OF A GRAPH

Kumar Abhishek$^1$, Ashwin Ganesan$^2$
$^{1,2}$Amrita School of Engineering
Amrita Vishwa Vidyapeetham
Coimbatore, 641 112, Tamil Nadu, INDIA


Abstract. For a simple connected graph $G = (V, E),$ let $M\subseteq V$ and $u \in V.$ The $M$-detour distance pattern of $G$ is the set $f_M(u) = \{D(u, v) : v \in M\}.$ If $f_M$ is injective function, then the set $M$ is a detour distance pattern distinguishing set (or, ddpd- set in short) of $G.$ A graph $G$ is defined as detour distance pattern distinguishing (or, ddpd-) graph if it admits a ddpd-set. The objective of this article is to initiate the study of graphs that admit marker set $M$ for which $f_M$ is injective. This article establishes some general results on ddpd-graphs.

Received: April 9, 2013

AMS Subject Classification: 05C22

Key Words and Phrases: detour distance, detour distance pattern, detour distance pattern distinguishing set

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DOI: 10.12732/ijpam.v87i5.5 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 87
Issue: 5