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A skew-symmetric graph may equivalently be defined as the double covering graph of a polar graph or switch graph, [1] which is an undirected graph in which the edges incident to each vertex are partitioned into two subsets. Each vertex of the polar graph corresponds to two vertices of the skew-symmetric graph, and each edge of the polar graph ...
Another problem related to reachability queries is in quickly recalculating changes to reachability relationships when some portion of the graph is changed. For example, this is a relevant concern to garbage collection which needs to balance the reclamation of memory (so that it may be reallocated) with the performance concerns of the running ...
Determine the x and y intercepts of the curve. The x intercepts are found by setting y equal to 0 in the equation of the curve and solving for x. Similarly, the y intercepts are found by setting x equal to 0 in the equation of the curve and solving for y. Determine the symmetry of the curve.
A t-transitive graph is a graph such that the automorphism group acts transitively on t-arcs, but not on (t + 1)-arcs. Since 1-arcs are simply edges, every symmetric graph of degree 3 or more must be t-transitive for some t, and the value of t can be used to further classify symmetric graphs.
The easier problem of testing whether a graph has any symmetries (nontrivial automorphisms), known as the graph automorphism problem, also has no known polynomial time solution. [5] There is a polynomial time algorithm for solving the graph automorphism problem for graphs where vertex degrees are bounded by a constant. [ 6 ]
The horizontal symmetry of the Mandelbrot set allows for portions of the rendering process to be skipped upon the presence of the real axis in the final image. However, regardless of the portion that gets mirrored, the same number of points will be rendered. Julia sets have symmetry around the origin.
However, because a given graph may correspond to more than one face lattice, it is difficult to extend this completeness result to the problem of recognizing the graphs of 4-polytopes. Determining the computational complexity of this graph recognition problem remains open. [40]
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric , combinatoric , or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra , the use of group theory , and the study of graph invariants .
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