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A radio antipodal coloring of a connected graph with diameter is an assignment of positive integers to the vertices of , with assigned , such that
for every two distinct vertices , of , where is the distance between and in . The radio antipodal coloring number of a radio antipodal coloring of is the maximum color assigned to a vertex of . The radio antipodal chromatic number of is over all radio antipodal colorings of . Radio antipodal chromatic numbers of paths...
Let G be a graph of order n and size m. A γ-labeling of G is a one-to-one function f:V(G) → 0,1,2,...,m that induces a labeling f’: E(G) → 1,2,...,m of the edges of G defined by f’(e) = |f(u)-f(v)| for each edge e = uv of G. The value of a γ-labeling f is . The maximum value of a γ-labeling of G is defined as
;
while the minimum value of a γ-labeling of G is
;
The values and are determined for double stars . We present characterizations of connected graphs G of order n for which or .
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