Table of Contents
What is semi graph in graph theory?
In the mathematical field of graph theory, a semi-symmetric graph is an undirected graph that is edge-transitive and regular, but not vertex-transitive.
What is a symmetric directed graph?
Symmetric directed graphs are directed graphs where all edges are bidirected (that is, for every arrow that belongs to the digraph, the corresponding inversed arrow also belongs to it).
What is a semi eulerian graph?
Definition: A graph is considered Semi-Eulerian if it is connected and there exists an open trail containing every edge of the graph (exactly once as per the definition of a trail). You do not need to return to the start vertex. Definition: A Semi-Eulerian trail is a trail containing every edge in a graph exactly once.
What is a semi-Hamiltonian graph?
A semi-Hamiltonian graph is a graph that contains a Hamiltonian path, but not a Hamilton cycle.
How do you know if data is symmetric?
A set of data is symmetric if the mean, median, and mode all occur at the same number. When graphed, the two sides of the graph will be almost mirror images of one another.
What is a symmetric histogram?
A symmetric histogram is a histogram for which the mean and the median are equal. If we draw a line through the center of a symmetric histogram it will get divided into two equal halves. The two halves will be identical mirror images of each other. A symmetric histogram is said to have zero skewness (no skewness).
Is a tree a complete graph?
True or false? A tree is a complete graph. The statement is false. A tree does not have an edge between each pair of its vertices.
What is the difference between semi Eulerian and Eulerian?
If there are exactly two vertices of odd degree, all Eulerian trails start at one of them and end at the other. A graph that has an Eulerian trail but not an Eulerian circuit is called semi-Eulerian.
How can you tell if a graph is Hamiltonian or semi Hamiltonian?
That path is called a “Hamiltonian cycle”. Like the graph 2 above, if a graph has a path that includes every vertex exactly once, but ending at another vertex than the starting one, then the graph is semi-Hamiltonian (is a semi-Hamiltonian graph).
What is Euler and Hamilton graph?
Definition. A cycle that travels exactly once over each edge in a graph is called “Eulerian.” A cycle that travels exactly once over each vertex in a graph is called “Hamiltonian.”
What is an example of symmetric data?
A symmetrical distribution is one where splitting the data down the middle produces mirror images. Bell curves are a commonly-cited example of symmetrical distributions.
Which graph is not a tree?
A tree will not contain a cycle, so if there is any cycle in the graph, it is not a tree. We can check it using another approach, if the graph is connected and it has V-1 edges, it could be a tree.
What is a semi-symmetric graph?
In the mathematical field of graph theory, a semi-symmetric graph is an undirected graph that is edge-transitive and regular, but not vertex-transitive.
Can a symmetric graph be an edge-transitive graph?
Symmetric graph. Since the definition above maps one edge to another, a symmetric graph must also be edge-transitive. However, an edge-transitive graph need not be symmetric, since a — b might map to c — d, but not to d — c. Semi-symmetric graphs, for example, are edge-transitive and regular, but not vertex-transitive.
What is a non-cubic symmetric graph?
Non-cubic symmetric graphs include cycle graphs (of degree 2), complete graphs (of degree 4 or more when there are 5 or more vertices), hypercube graphs (of degree 4 or more when there are 16 or more vertices), and the graphs formed by the vertices and edges of the octahedron, icosahedron, cuboctahedron, and icosidodecahedron.
How do you know if a graph is symmetric?
In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1 — v1 and u2 — v2 of G, there is an automorphism f ( u1) = u2 and f ( v1) = v2.