Some Resolving Parameters in a Class of Cayley Graphs

Domination parameters of Cayley graphs of some groups

‎In this paper‎, ‎we investigate domination number‎, ‎$gamma$‎, ‎as well‎ ‎as signed domination number‎, ‎$gamma_{_S}$‎, ‎of all cubic Cayley‎ ‎graphs of cyclic and quaternion groups‎. ‎In addition‎, ‎we show that‎ ‎the domination and signed domination numbers of cubic graphs depend‎ on each other‎.

Cayley graphs and G-graphs: Some applications

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...

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...

Some properties of unitary addition Cayley graphs

Let Γ be an abelian group and B be a subset of Γ. The addition Cayley graph G′ = Cay(Γ, B) is the graph having the vertex set V (G′) = Γ and the edge set E(G′) = {ab : a + b ∈ B}, where a, b ∈ Γ. For a positive integer n > 1, the unitary addition Cayley graph Gn is the graph whose vertex set is Zn, the integers modulo n and if Un denotes set of all units of the ring Zn, then two vertices a, b a...