Predavateljica: Sylwia Cichacz
A emph{group distance magic labeling} or a $gr$-distance magic labeling of a graph $G(V,E)$ with $|V | = n$ is an injection $f$ from $V$ to an Abelian group $gr$ of order $n$ such that the weight $w(x)=sum_{yin N_G(x)}f(y)$ of every vertex $x in V$ is equal to the same element $mu in gr$, called the magic constant.
In the talk it will be presented that if $G$ is a graph of order $n=2^{p}(2k+1)$ for some natural numbers $p$, $k$ such that $deg(v)equiv c imod {2^{p+1}}$ for some constant $c$ for any $vin V(G)$, then there exists an $gr$-distance magic labeling for any abelian group $gr$ for the graph $G[C_4]$. Moreover we prove that if $gr$ is an arbitrary abelian group of order $4n$ such that $gr cong zet_2 timeszet_2 times gA$ for some abelian group $gA$ of order $n$, then exists a $gr$-distance magic labeling for any graph $G[C_4]$.
In the talk it will be presented that if $G$ is a graph of order $n=2^{p}(2k+1)$ for some natural numbers $p$, $k$ such that $deg(v)equiv c imod {2^{p+1}}$ for some constant $c$ for any $vin V(G)$, then there exists an $gr$-distance magic labeling for any abelian group $gr$ for the graph $G[C_4]$. Moreover we prove that if $gr$ is an arbitrary abelian group of order $4n$ such that $gr cong zet_2 timeszet_2 times gA$ for some abelian group $gA$ of order $n$, then exists a $gr$-distance magic labeling for any graph $G[C_4]$.
