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In graph-theoretic mathematics, a biregular graph or semiregular bipartite graph is a bipartite graph G = ( U , V , E ) {\displaystyle G=(U,V,E)} for which
Biregular_graph
Graph divided into two independent sets
balanced bipartite graph. If all vertices on the same side of the bipartition have the same degree, then G {\displaystyle G} is called biregular. When modelling
Bipartite_graph
{\sqrt {|S||T|(1-|S|/n)(1-|T|/n)}}\,} using similar techniques. For biregular graphs, we have the following variation, where we take λ {\displaystyle \lambda
Expander_mixing_lemma
However, unless the graph is connected, it may not have a unique 2-coloring. biregular A biregular graph is a bipartite graph in which there are only
Glossary_of_graph_theory
Graph representing incident points and lines
bipartite graph with girth at least six can be viewed as the Levi graph of an abstract incidence structure. Levi graphs of configurations are biregular, and
Levi_graph
Every graph has evenly many odd vertices
equals the number of edges in the graph. In particular, both subsets have equal degree sums. For biregular graphs, with a partition of the vertices into
Handshaking_lemma
Concept in graph theory
In graph theory, a strongly regular graph (SRG) is a regular graph G = (V, E) with v vertices and degree k such that for some given integers λ , μ ≥ 0
Strongly_regular_graph
Number of edges touching a vertex in a graph
bipartition as each other have the same degree is called a biregular graph. An undirected, connected graph has an Eulerian path if and only if it has either 0
Degree_(graph_theory)
Graph where all pairs of edges are automorphic
either semi-symmetric or biregular. Examples of edge but not vertex transitive graphs include the complete bipartite graphs K m , n {\displaystyle K_{m
Edge-transitive_graph
Branch of mathematics
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatorial
Algebraic_graph_theory
Graph defined from a mathematical group
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract
Cayley_graph
Argentine-born American mathematician
different biregular graph whose bipartition is formed by the vertices and 5-cycles of the Petersen graph. A perfect dominating set S of a graph G is a set
Italo_Jose_Dejter
Directed graph isomorphic to its own transpose graph
In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by
Skew-symmetric_graph
Graph property
In the mathematical field of graph theory, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices
Distance-regular_graph
Graph where any two nodes of equal distance are isomorphic
In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any
Distance-transitive_graph
Graph where each vertex has the same number of neighbors
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular
Regular_graph
missing publisher (link). O. Reingold and L. Trevisan and S. Vadhan. Pseudorandom walks in biregular graphs and the RL vs. L problem, ECCC TR05-022, 2004.
RL_(complexity)
Graph where all pairs of vertices are automorphic
regular graphs are vertex-transitive (for example, the Frucht graph and Tietze's graph). Finite vertex-transitive graphs include the symmetric graphs (such
Vertex-transitive_graph
Type of graph in graph theory
of graph theory, a half-transitive graph is a graph that is both vertex-transitive and edge-transitive, but not symmetric. In other words, a graph is
Half-transitive_graph
Undirected graph with no non-trivial symmetries
In graph theory, a branch of mathematics, an undirected graph is called an asymmetric graph if it has no nontrivial symmetries. Formally, an automorphism
Asymmetric_graph
Type of error-correcting codes
exist). Let B {\displaystyle B} be a ( c , d ) {\displaystyle (c,d)} -biregular graph between a set of n {\displaystyle n} nodes { v 1 , ⋯ , v n } {\displaystyle
Expander_code
Graph in which all ordered pairs of linked nodes are automorphic
In the mathematical field of graph theory, a graph G is symmetric or arc-transitive if, given any two ordered pairs of adjacent vertices ( u 1 , v 1 )
Symmetric_graph
Graph that is edge-transitive and regular but not vertex-transitive
graph theory, a semi-symmetric graph is an undirected graph that is edge-transitive and regular, but not vertex-transitive. In other words, a graph is
Semi-symmetric_graph
Coloring in which edges are labeled by integers
coloring. For any planar interval colorable graph G on n vertices t(G)≤(11/6)n. A bipartite graph is (a, b)-biregular if everyvertex in one part has degree
Interval_edge_coloring
In the mathematical field of graph theory, a zero-symmetric graph is a connected graph in which each vertex has exactly three incident edges and, for
Zero-symmetric_graph
Points and lines with equal incidences
latter case they are closely related to regular hypergraphs and biregular bipartite graphs, but with some additional restrictions: every two points of the
Configuration_(geometry)
Construction in group theory
Cr(Pn(k)) of birational automorphisms; any biregular automorphism is linear, so PGL coincides with the group of biregular automorphisms. Projective transformation
Projective_linear_group
Structure in combinatorial mathematics
Also, each configuration has a corresponding biregular bipartite graph known as its incidence or Levi graph. Given a finite set X (of elements called points)
Block_design
Discrete subgroup in a locally compact topological group
of automorphisms; for example, T {\displaystyle T} can be a regular or biregular tree. The group of automorphisms A u t ( T ) {\displaystyle \mathrm {Aut}
Lattice_(discrete_subgroup)
Principle in geometry
in general linear position, which is true because the Veronese map is biregular: i.e., if the image of five points satisfy a relation, then the relation
Five_points_determine_a_conic
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BIREGULAR GRAPH
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BIREGULAR GRAPH
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BIREGULAR GRAPH
BIREGULAR GRAPH
BIREGULAR GRAPH
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