Some problems on Cayley graphs

Some problems on Cayley graphs

This survey paper presents the historical development of some problems on Cayley graphs which are interesting to graph and group theorists such as Hamiltonicity or diameter problems, to computer scientists and molecular biologists such as pancake problem or sorting by reversals, to coding theorists such as the vertex reconstruction problem related to error-correcting codes but not related to Ul...

Lecture notes on some problems on Cayley graphs

On the zero forcing number of some Cayley graphs

‎Let Γa be a graph whose each vertex is colored either white or black‎. ‎If u is a black vertex of Γ such that exactly one neighbor‎ ‎v of u is white‎, ‎then u changes the color of v to black‎. ‎A zero forcing set for a Γ graph is a subset of vertices Zsubseteq V(Γ) such that‎ if initially the vertices in Z are colored black and the remaining vertices are colored white‎, ‎then Z changes the col...

Cayley graphs and G-graphs: Some applications

On two-dimensional Cayley graphs

A subset W of the vertices of a graph G is a resolving set for G when for each pair of distinct vertices u,v in V (G) there exists w in W such that d(u,w)≠d(v,w). The cardinality of a minimum resolving set for G is the metric dimension of G. This concept has applications in many diverse areas including network discovery, robot navigation, image processing, combinatorial search and optimization....