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Radio antipodal colorings of graphs

Gary ChartrandDavid ErwinPing Zhang — 2002

Mathematica Bohemica

A radio antipodal coloring of a connected graph G with diameter d is an assignment of positive integers to the vertices of G , with x V ( G ) assigned c ( x ) , such that d ( u , v ) + | c ( u ) - c ( v ) | d for every two distinct vertices u , v of G , where d ( u , v ) is the distance between u and v in G . The radio antipodal coloring number a c ( c ) of a radio antipodal coloring c of G is the maximum color assigned to a vertex of G . The radio antipodal chromatic number a c ( G ) of G is min { a c ( c ) } over all radio antipodal colorings c of G . Radio antipodal chromatic numbers of paths...

On γ-labelings of trees

Gary ChartrandDavid ErwinDonald W. VanderJagtPing Zhang — 2005

Discussiones Mathematicae Graph Theory

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 v a l ( f ) = Σ e E ( G ) f ' K ( e ) . The maximum value of a γ-labeling of G is defined as v a l m a x ( G ) = m a x v a l ( f ) : f i s a γ - l a b e l i n g o f G ; while the minimum value of a γ-labeling of G is v a l m i n ( G ) = m i n v a l ( f ) : f i s a γ - l a b e l i n g o f G ; The values v a l m a x ( S p , q ) and v a l m i n ( S p , q ) are determined for double stars S p , q . We present characterizations of connected graphs G of order n for which v a l m i n ( G ) = n or v a l m i n ( G ) = n + 1 .

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