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Locating Codes and Locating Numbers of Graphs

Dr. Shane Redmond

Dr. Shane Redmond / Eastern Kentucky University

Given a connected graph G and an ordered subset W of the vertex set of G, we define the locating code of a vertex v of G to be the vector representing the distances from v to the vertices of W.  The set W is called a locating set if distinct vertices have distinct codes. The minimum cardinality for a locating set G is called the locating number of G. We will do lots of examples to illustrate this concept.  Then, we will discuss ways to find locating sets and calculate locating numbers. Finally, we will apply these topics to zero-divisor graphs of commutative rings.

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