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The circular ladder graph CL n is constructible by connecting the four 2-degree vertices in a straight way, or by the Cartesian product of a cycle of length n ≥ 3 and an edge. [4] In symbols, CL n = C n × P 2. It has 2n nodes and 3n edges. Like the ladder graph, it is connected, planar and Hamiltonian, but it is bipartite if and only if n is ...
A graph is said to be k-generated if for every subgraph H of G, the minimum degree of H is at most k. Incidence chromatic number of k-degenerated graphs G is at most ∆(G) + 2k − 1. Incidence chromatic number of K 4 minor free graphs G is at most ∆(G) + 2 and it forms a tight bound. Incidence chromatic number of a planar graph G is at most ...
The Cartesian product of two edges is a cycle on four vertices: K 2 K 2 = C 4. The Cartesian product of K 2 and a path graph is a ladder graph. The Cartesian product of two path graphs is a grid graph. The Cartesian product of n edges is a hypercube: =.
In graph theory, the Möbius ladder M n, for even numbers n, is formed from an n-cycle by adding edges (called "rungs") connecting opposite pairs of vertices in the cycle. It is a cubic, circulant graph, so-named because (with the exception of M 6 (the utility graph K 3,3), M n has exactly n/2 four-cycles [1] which link together by their shared edges to form a topological Möbius strip.
This type of mapping between graphs is the one that is most commonly used in category-theoretic approaches to graph theory. A proper graph coloring can equivalently be described as a homomorphism to a complete graph. 2. The homomorphism degree of a graph is a synonym for its Hadwiger number, the order of the largest clique minor. hyperarc
Below is the table of the vertex numbers for the best-known graphs (as of July 2022) in the undirected degree diameter problem for graphs of degree at most 3 ≤ d ≤ 16 and diameter 2 ≤ k ≤ 10. Only a few of the graphs in this table (marked in bold) are known to be optimal (that is, largest possible).
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