Irregularity and Modular Irregularity Strength of Wheels

It is easily observed that the vertices of a simple graph cannot have pairwise distinct degrees. This means no order at least two is, in this way, irregular. However, multigraph can be Chartrand et al., 1988, posed following problem: loopless multigraph, how one determine fewest parallel edges required to ensure all degrees? problem known as labeling and, for its solution, al. introduced irregular assignments. The irregularity strength G maximal edge label used an assignment, minimized over Thus, equal smallest maximum multiplicity create from G. In present paper, we show existence scheme proves exact value wheels. Then, modify mapping six cases and obtain labelings modular wheels natural modification strength.