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Paper Information

Journal:   TRANSACTIONS ON COMBINATORICS   2014 , Volume 3 , Number 4; Page(s) 19 To 30.
 
Paper: 

THE GEODETIC DOMINATION NUMBER FOR THE PRODUCT OF GRAPHS

 
 
Author(s):  ROBINSON CHELLATHURAI S., PADMA VIJAYA S.*
 
* DEPARTMENT OF MATHEMATICS, UNIVERSITY COLLEGE OF ENGINEERING NAGERCOIL, ANNA UNIVERSITY, TIRUNELVELI REGION, NAGERCOIL, INDIA
 
Abstract: 

A subset S of vertices in a graph G is called a geodetic set if every vertex not in S lies on a shortest path between two vertices from S. A subset D of vertices in G is called dominating set if every vertex not in D has at least one neighbor in D. A geodetic dominating set S is both a geodetic and a dominating set. The geodetic (domination, geodetic domination) number g(G) (g(G), gg (G)) of G is the minimum cardinality among all geodetic (dominating, geodetic dominating) sets in G. In this paper, we show that if a triangle free graph G has minimum degree at least 2 and g (G) =2, then gg(G) = g(G). It is shown, for every nontrivial connected graph G with g (G) =2 and diam (G)>3, that gg (G)>g (G). The lower bound for the geodetic domination number of Cartesian product graphs is proved. Geodetic domination number of product of cycles (paths) are determined. In this work, we also determine some bounds and exact values of the geodetic domination number of strong product of graphs.

 
Keyword(s): CARTESIAN PRODUCT, STRONG PRODUCT, GEODETIC NUMBER, DOMINATION NUMBER, GEODETIC DOMINATION NUMBER
 
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