### Maximum difference about the size of optimal identifying codes in graphs differing by one vertex

*Mikko Pelto*

#### Abstract

Let G=(V,E) be a simple undirected graph. We call any
subset C⊆V an identifying code if the sets
I(v)={c∈C | {v,c}∈E or
v=c } are distinct and non-empty for all
vertices v∈V. A graph is called twin-free if there
is an identifying code in the graph. The identifying code with minimum
size in a twin-free graph G is called the optimal
identifying code and the size of such a code is denoted by
γ(G). Let G

_{S}denote the induced subgraph of G where the vertex set S⊂V is deleted. We provide a tight upper bound for γ(G_{S})-γ(G) when both graphs are twin-free and |V| is large enough with respect to |S|. Moreover, we prove tight upper bound when G is a bipartite graph and |S|=1.Full Text: PDF PostScript