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A Lower Bound and Several Exact Results on the -Lucky Number
If is a vertex labeling of a graph , then the -lucky sum of a vertex is . The labeling is a -lucky labeling
if for every . The -lucky number
of is the least positive integer such that has a
-lucky labeling . A general lower bound on the
-lucky number of a graph in terms of its clique number and related degree
invariants is proved. The bound is sharp as demonstrated with an infinite
family of corona graphs. The -lucky number is also determined for the
so-called -web graphs and graphs obtained by attaching the same number
of pendant vertices to the vertices of a generalized cocktail-party graph