# Title

THE DETOUR IRREDUNDANT NUMBER OF A GRAPH

# Authors

S. Delbin Prema, C. Jayasekaran
Department of Mathematics
RVS Technical Campus - Coimbatore
Coimbatore, 641402, Tamil Nadu, INDIA
Department of Mathematics
Pioneer Kumaraswamy College
Nagercoil, 629003, Tamil Nadu, INDIA

# Abstract

For two vertices and of a connected graph , the set consists of all those vertices lying on detour in . Given a set of vertices of , the union of all sets for is denoted by . A detour convex set satisfies . The detour convex hull of is the smallest detour convex set containing . The detour hull number is the minimum cardinality among the subsets of with . In this paper, we introduce and study the detour irredundant number of a graph. A set of vertices of is a detour irredundant set if for all and the maximum cardinality of a detour irredudant set is its detour irredundant number of . We determine the detour irredundant number of certain standard classes of graphs. Certain general properties of these concepts are studied. We characterize the classes of graphs of order for which or or , respectvely. We prove that for any integers and with , there exists a connected graph such that and . We also prove that for integers and with , there exists a connected graph with and .

# History

Received: March 20, 2017
Revised: June 5, 2018
Published: June 5, 2018

# AMS Classification, Key Words

AMS Subject Classification: 05C12
Key Words and Phrases: detour convex set, extreme vertex, detour hull number, detour irredundant sets, detour irredundant number

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## Bibliography

1
F. Buckley and F. Harary, Distance in Graphs, Addison-Wesley, ReadingMA, (1990).

2
G. Chartrand and P. Zhang, Introduction to Graph Theory, Tata McGraw- Hill Edition, New Delhi,2006.

# How to Cite?

DOI: 10.12732/ijpam.v119i1.4 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: 2018
Volume: 119
Issue: 1
Pages: 53 - 62