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An arc-transitive graph, sometimes also called a flag-transitive graph, is a graph whose graph automorphism group acts transitively on its graph arcs (Godsil and Royle 2001, ...

There are a number of meanings for the word "arc" in mathematics. In general, an arc is any smooth curve joining two points. The length of an arc is known as its arc length. ...

A relation R on a set S is transitive provided that for all x, y and z in S such that xRy and yRz, we also have xRz.

An arc of a graph, sometimes also called a flag, is an ordered pair of adjacent vertices (Godsil and Royle 2001, p. 59), sometimes also called a directed line (Harary 1994, ...

Let (X,tau) be a topological space, and let p in X. Then the arc component of p is union {A subset= X:A is an arc and p in A}.

A major arc (right figure) is an arc of a circle having measure greater than or equal to 180 degrees (pi radians).

A minor arc (left figure) is an arc of a circle having measure less than or equal to 180 degrees (pi radians).

A unit of angular measure equal to 60 arc seconds, or 1/60 of a degree. The arc minute is denoted ^' (not to be confused with the symbol for feet).

The arc set of a directed graph is the set of all arcs (directed edges) of the graph. The arc set for a directed graph g is given in the Wolfram Language by EdgeList[g].

The transitive reduction of a binary relation R on a set X is the minimum relation R^' on X with the same transitive closure as R. Thus aR^'b for any elements a and b of X, ...