The independent resolving number of a graph
 
 
Description:  For an ordered set W{w_1,w_2,...,w_k} of vertices in a connected graph G and a vertex v of G, the code with respect to W is the k-vector c_W(v)=(d(v,w_1),d(v,w_2),..., d(v,w_k)). The set W is an independent resolving set for G if W is independent in G and distinct vertices have distinct codes with respect to W. The cardinality of a minimum independent resolving set in G is the independent resolving number ir G. We study the existence of independent resolving sets in graphs, characterize all nontrivial connected graphs G of order n with ir G=1,n-1,n-2, and present several realization results. It is shown that for every pair r,k of integers with k\geq 2 and 0\leq r\leq k, there exists a connected graph G with ir G=k such that exactly r vertices belong to every minimum independent resolving set of G.
Area(s):
Date:  2006-10-31
Start Time:   14:45
Speaker:  Varaporn Saenpholphat (Srinahkarinwirot Univ, Thailand)
Place:  Sala 2.4
Research Groups: -Algebra and Combinatorics
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