Vertex Magic Labeling On V_4 for Cartesian product of two cycles

Group distance magic labeling of Cartesian product of cycles

A group distance magic labeling of a graph G(V, E) with |V | = n is an injection from V to an abelian group Γ of order n such that the sum of labels of all neighbors of every vertex x ∈ V is equal to the same element μ ∈ Γ. We completely characterize all Cartesian products Ck Cm that admit a group distance magic labeling by Zkm.

Vertex magic total labeling of products of cycles

Hyperhamiltonicity Of The Cartesian Product Of Two Directed Cycles

Let Za × Zb be the product of two directed cycles, let Zc be a subgroup of Za, and let Zd be a subgroup of Zb. Also, let A = a c and B =

Coloring the square of the Cartesian product of two cycles

The square G2 of a graph G is defined on the vertex set of G in such a way that distinct vertices with distance at most two in G are joined by an edge. We study the chromatic number of the square of the Cartesian product Cm2Cn of two cycles and show that the value of this parameter is at most 7 except when m = n = 3, in which case the value is 9, and when m = n = 4 or m = 3 and n = 5, in which ...

Vertex-magic labeling of non-regular graphs

In this paper, we are studying vertex-magic total labelings (VMTLs) of simple graphs. By now much is known about methods for constructing VMTLs for regular graphs. Here we are studying non-regular graphs. We show how to construct labelings for several families of non-regular graphs, including graphs formed as the disjoint union of two other graphs already possessing VMTLs. We focus on condition...