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In graph theory, a branch of combinatorial mathematics, a block graph or clique tree [1] is a type of undirected graph in which every biconnected component (block) is a clique. Block graphs are sometimes erroneously called Husimi trees (after Kôdi Husimi ), [ 2 ] but that name more properly refers to cactus graphs , graphs in which every ...
A simplex graph is an undirected graph κ(G) with a vertex for every clique in a graph G and an edge connecting two cliques that differ by a single vertex. It is an example of median graph , and is associated with a median algebra on the cliques of a graph: the median m ( A , B , C ) of three cliques A , B , and C is the clique whose vertices ...
The block graph of a given graph G is the intersection graph of its blocks. Thus, it has one vertex for each block of G, and an edge between two vertices whenever the corresponding two blocks share a vertex. A graph H is the block graph of another graph G exactly when all the blocks of H are complete subgraphs.
Every edge of a graph belongs in exactly one block. 2. The block graph of a graph G is another graph whose vertices are the blocks of G, with an edge connecting two vertices when the corresponding blocks share an articulation point; that is, it is the intersection graph of the blocks of G. The block graph of any graph is a forest. 3.
In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge.The neighbourhood of a vertex v in a graph G is the subgraph of G induced by all vertices adjacent to v, i.e., the graph composed of the vertices adjacent to v and all edges connecting vertices adjacent to v.
In the mathematical discipline of graph theory, the 2-factor theorem, discovered by Julius Petersen, is one of the earliest works in graph theory. It can be stated as follows: [ 1 ] Let G {\displaystyle G} be a regular graph whose degree is an even number, 2 k {\displaystyle 2k} .
The block designed with their for both mathematics and play in mind. The advice given in the 1968 EDC Teacher's Guide is: "Take out the blocks, and play with them yourself. Try out some of your own ideas. Then, when you give the blocks to the children, sit back and watch what they do."
Every cluster graph is a block graph, a cograph, and a claw-free graph. [1] Every maximal independent set in a cluster graph chooses a single vertex from each cluster, so the size of such a set always equals the number of clusters; because all maximal independent sets have the same size, cluster graphs are well-covered.
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