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8 papers · 1 filter
Vertex and edge orbits of Fibonacci and Lucas cubes
Ali Reza Ashrafi, Jernej Azarija, Khadijeh Fathalikhani +2
The Fibonacci cube is obtained from the -cube by removing all the vertices that contain two consecutive 1s. If, in addition, the vertices that start and end with 1 a…
Moore graphs and cycles are extremal graphs for convex cycles
Jernej Azarija, Sandi Klavžar
Let denote the number of convex cycles of a simple graph G of order n, size m, and girth 3 <= g <=n. It is proved that and that equality holds…
Domination game played on trees and spanning subgraphs
Bostjan Bresar, Sandi Klavzar, Douglas F. Rall
The domination game is played on a graph G. Vertices are chosen, one at a time, by two players Dominator and Staller. Each chosen vertex must enlarge the set of vertices of G domin…
Rainbow domination in the lexicographic product of graphs
Tadeja Kraner Sumenjak, Douglas F. Rall, Aleksandra Tepeh
Let k be a positive integer and let f be a map from V(G) to the set of all subsets of {1,2,3,...,k}. The function f is called a k-rainbow dominating function of G provided that whe…
A characterization of the edge connectivity of direct products of graphs
Simon Spacapan
The direct product of graphs and is the graph, denoted as , with vertex set , where vertices an…
Minimum k-path vertex cover
Boštjan Brešar, František Kardoš, Ján Katrenič +1
A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. Denote by ψ_k(G) the minimum cardinality of a…