Note that conventionally the term "symmetric graph" is not complementary to the term " asymmetric graph," as the latter refers to a graph that has no nontrivial symmetries at all.

Aug 3, 2023 · A graph is said to have symmetry if it can divided into two equal parts along a line such that one part is an exact mirror image of the other. The concept is useful to graph an …

5 days ago · A symmetric graph is a graph that is both edge- and vertex-transitive (Holton and Sheehan 1993, p. 209). However, care must be taken with this definition since arc-transitive or …

Demonstrates how to recognize symmetry in graphs, in particular with respect to the y-axis and the origin.

Nov 16, 2022 · In this section we introduce the idea of symmetry. We discuss symmetry about the x-axis, y-axis and the origin and we give methods for determining what, if any symmetry, a …

Jun 13, 2025 · Explore the concept of symmetric graphs, their properties, and applications in graph theory and real-world problems.

Another way to visualize origin symmetry is to imagine a reflection about the x -axis, followed by a reflection across the y -axis. If this leaves the graph of the function unchanged, the graph is …

Oct 6, 2021 · We say that a graph is symmetric with respect to the x axis if for every point (a, b) on the graph, there is also a point (a, b) on the graph; hence (1.2.2) f (x, y) = f (x, y)

Forming part of algebraic graph theory, this fast-growing field is concerned with the study of highly symmetric graphs, particularly vertex-transitive graphs, and other combinatorial structures, …

Symmetry is one of the most important aesthetic criteria that clearly reveals the structure and properties of a graph. Graphs in textbooks on graph theory are normally drawn sym-metrically. …