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The Grötzsch graph is a member of an infinite sequence of triangle-free graphs, each the Mycielskian of the previous graph in the sequence, starting from the one-edge graph; this sequence of graphs was constructed by Mycielski (1955) to show that there exist triangle-free graphs with arbitrarily large chromatic number. Therefore, the Grötzsch ...
This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...
In chemical graph theory, the Wiener index (also Wiener number) introduced by Harry Wiener, is a topological index of a molecule, defined as the sum of the lengths of the shortest paths between all pairs of vertices in the chemical graph representing the non-hydrogen atoms in the molecule.
A native graph system with index-free adjacency does not have to move through any other type of data structures to find links between the nodes. Directly related nodes in a graph are stored in the cache once one of the nodes are retrieved, making the data lookup even faster than the first time a user fetches a node. However, such advantage ...
In information theory, the graph entropy is a measure of the information rate achievable by communicating symbols over a channel in which certain pairs of values may be confused. [1] This measure, first introduced by Körner in the 1970s, [ 2 ] [ 3 ] has since also proven itself useful in other settings, including combinatorics.
By 2007, the captive population comprised 239 giant pandas in China and another 27 outside the country. It has often served as China's national symbol, appeared on Chinese Gold Panda coins since 1982 and as one of the five Fuwa mascots of the 2008 Summer Olympics held in Beijing.