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...

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...

Edge-transitive graph Lovász conjecture Semi-symmetric graph Zero-symmetric graph Godsil, Chris; Royle, Gordon (2013) [2001], Algebraic Graph Theory, Graduate...

each column sums to zero since A D + {\displaystyle AD^{+}} is left stochastic. For a non-symmetric adjacency matrix of a directed graph, one also needs to...

matrix is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory....

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...

regular graph is a distance-regular graph with diameter 2 whenever μ is non-zero. It is a locally linear graph whenever λ = 1. A strongly regular graph is...

mathematical field of graph theory, the term "null graph" may refer either to the order-zero graph, or alternatively, to any edgeless graph (the latter is sometimes...

other automorphisms. Note that the term "asymmetric graph" is not a negation of the term "symmetric graph," as the latter refers to a stronger condition than...

to be symmetric ( S = S − 1 {\displaystyle S=S^{-1}} ) and not containing the group identity element. In this case, the uncolored Cayley graph can be...

maximum size of the graph is n(n − 1)/2. The edges of an undirected simple graph permitting loops G {\displaystyle G} induce a symmetric homogeneous relation...

called loop-digraphs (see section Types of directed graph). Symmetric directed graphs are directed graphs where all edges appear twice, one in each direction...

families of graphs based on symmetry (such as symmetric graphs, vertex-transitive graphs, edge-transitive graphs, distance-transitive graphs, distance-regular...

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...

and symmetric are guaranteed to be Eulerian. However, this is not a necessary condition, as it is possible to construct a non-symmetric, even graph that...

the Petersen graph has non-orientable genus 1. The Petersen graph is strongly regular (with signature srg(10,3,0,1)). It is also symmetric, meaning that...

In the mathematical field of graph theory, the Möbius–Kantor graph is a symmetric bipartite cubic graph with 16 vertices and 24 edges named after August...

{\displaystyle 2k} nonzero eigenvalues. Note that the (simple) graph of a real symmetric or skew-symmetric matrix A {\displaystyle A} of order n {\displaystyle...

graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject...

dual graph is symmetric, meaning that if H is a dual of a connected graph G, then G is a dual of H. When discussing the dual of a graph G, the graph G itself...

products: Symmetric groups – The symmetric group Sn contains, for any group of order n, a subgroup isomorphic to that group. Thus the cycle graph of every...

for negative input (y<0) to avoid the singularity for zero input (y=0), and so produce symmetric log plots: Y = sgn ⁡ ( y ) ⋅ log 10 ⁡ ( 1 + | y / C |...

For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set. The symmetric group is important to diverse areas of...

one vertex and zero edges. More generally, a component of this type is formed for every isolated vertex in any graph. In a connected graph, there is exactly...

describe properties of line-symmetric graphs. Note the obvious but important observation that every line-symmetric graph is line-regular. Karypis, G....

the OEIS) Edge-transitive graphs include all symmetric graph, such as the vertices and edges of the cube. Symmetric graphs are also vertex-transitive...

fields of characteristic zero, the graded vector space of all symmetric tensors can be naturally identified with the symmetric algebra on V. A related...

real functions whose graph is self-symmetric with respect to the y-axis, and odd functions are those whose graph is self-symmetric with respect to the...

equations coincident. Only certain roses are symmetric about the pole. Individual petals are symmetric about the line through the pole and the petal's...

{f(x+h)-2f(x)+f(x-h)}{h^{2}}}.} The limit is called the second symmetric derivative. The second symmetric derivative may exist even when the (usual) second derivative...