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A section of a graph obtained by finding its intersection with a plane.

Thus, all radio-waves have a color between 1mm and 10000km long. Relative to visible colors, they are “very very very” to “extremely terribly very” dark red.

In graph theory, a branch of mathematics, a radio coloring of an undirected graph is a form of graph coloring in which one assigns positive integer labels to the graphs such that the labels of adjacent vertices differ by at least two, and the labels of vertices at distance two from each other differ by at least one.

The radio number( rn ( G )) of G is thelowest span over all radio labelings of the graph. We will refer to inequality(1.1) as the radio condition. Note that this condition necessitates the useof distance integers, thus rn( G ) ≥ | V ( G ) | for all graphs G .

1. : a diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables. 2. : the collection of all points whose coordinates satisfy a given relation (such as a function)

In graph theory, a branch of mathematics, a radio coloring of an undirected graph is a form of graph coloring in which one assigns positive integer labels to the graphs such that the labels of adjacent vertices differ by at least two, and the labels of vertices at distance two from each other differ by at least one.

A radio labeling of a graph is labeling using distinct nonnegative integers such that for every pair of distinct vertices , in the vertex set of . Then the radio number of , commonly denoted , is the smallest integer such that has a radio labeling with .

The middle graph of a graph G, denoted by M(G), is the graph whose vertex set is V (G) ∪ E(G) and in which two vertices are adjacent if and only if either they are adjacent edges of G or one is a vertex of G and the other is an edge incident on it.

A section of a graph obtained by finding its intersection with a plane.

Thus, all radio-waves have a color between 1mm and 10000km long. Relative to visible colors, they are “very very very” to “extremely terribly very” dark red.

In graph theory, a branch of mathematics, a radio coloring of an undirected graph is a form of graph coloring in which one assigns positive integer labels to the graphs such that the labels of adjacent vertices differ by at least two, and the labels of vertices at distance two from each other differ by at least one.

The radio number( rn ( G )) of G is thelowest span over all radio labelings of the graph. We will refer to inequality(1.1) as the radio condition. Note that this condition necessitates the useof distance integers, thus rn( G ) ≥ | V ( G ) | for all graphs G .

1. : a diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables. 2. : the collection of all points whose coordinates satisfy a given relation (such as a function)

In graph theory, a branch of mathematics, a radio coloring of an undirected graph is a form of graph coloring in which one assigns positive integer labels to the graphs such that the labels of adjacent vertices differ by at least two, and the labels of vertices at distance two from each other differ by at least one.

A radio labeling of a graph is labeling using distinct nonnegative integers such that for every pair of distinct vertices , in the vertex set of . Then the radio number of , commonly denoted , is the smallest integer such that has a radio labeling with .

The middle graph of a graph G, denoted by M(G), is the graph whose vertex set is V (G) ∪ E(G) and in which two vertices are adjacent if and only if either they are adjacent edges of G or one is a vertex of G and the other is an edge incident on it.