7 research outputs found
Group Irregularity Strength of Connected Graphs
We investigate the group irregularity strength () of graphs, i.e. the
smallest value of such that taking any Abelian group \gr of order ,
there exists a function f:E(G)\rightarrow \gr such that the sums of edge
labels at every vertex are distinct. We prove that for any connected graph
of order at least 3, if and otherwise,
except the case of some infinite family of stars
Group Irregular Labelings of Disconnected Graphs
We investigate the \textit{group irregularity strength} () of graphs, i.e. the smallest value of such that taking any Abelian group \gr of order , there exists a function f:E(G)\rightarrow \gr such that the sums of edge labels at every vertex are distinct. We give the exact values and bounds on for chosen families of disconnected graphs. In addition we present some results for the \textit{modular edge gracefulness} , i.e. the smallest value of such that there exists a function f:E(G)\rightarrow \zet_s such that the sums of edge labels at every vertex are distinct