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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 ...
In graph theory, a geodetic graph is an undirected graph such that there exists a unique (unweighted) shortest path between each two vertices.. Geodetic graphs were introduced in 1962 by Øystein Ore, who observed that they generalize a property of trees (in which there exists a unique path between each two vertices regardless of distance), and asked for a characterization of them. [1]
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.
A block diagram is a diagram of a system in which the principal parts or functions are represented by blocks connected by lines that show the relationships of the blocks. [1] They are heavily used in engineering in hardware design , electronic design , software design , and process flow diagrams .
(formerly Build Your Own Blocks) is a free block-based educational graphical programming language and online community. Snap allows students to explore, create, and remix interactive animations, games, stories, and more, while learning about mathematical and computational ideas.
For k = 3, every k-critical graph (that is, every odd cycle) can be generated as a k-constructible graph such that all of the graphs formed in its construction are also k-critical. For k = 8 , this is not true: a graph found by Catlin (1979) as a counterexample to Hajós's conjecture that k -chromatic graphs contain a subdivision of K k , also ...
A partially balanced incomplete block design with n associate classes (PBIBD(n)) is a block design based on a v-set X with b blocks each of size k and with each element appearing in r blocks, such that there is an association scheme with n classes defined on X where, if elements x and y are ith associates, 1 ≤ i ≤ n, then they are together ...
The Lego system is the most widely used clamp building block system in the world. Building blocks (also construction blocks) are modular construction parts, usually made of plastic, which can be assembled in a form-fit manner. The basic components are usually cuboid-shaped, cylindrically studded at the top in a grid pattern, hollow-bodied at ...
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