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The material is press-ready and may be printed by paying a 5% royalty, and by acknowledging NCERT. [11] The textbooks are in color-print and are among the least expensive books in Indian book stores. [11] Textbooks created by private publishers are priced higher than those of NCERT. [11]
A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. [2] A directed tree, [3] oriented tree, [4] [5] polytree, [6] or singly connected network [7] is a directed acyclic graph (DAG) whose underlying undirected graph is ...
MyMaths is a subscription-based mathematics website which can be used on interactive whiteboards or by students and teachers at home. [1] [2] It is owned and operated by Oxford University Press, who acquired the site in 2011. As of February 2021, MyMaths has over 4 million student users in over 70 countries worldwide. [3]
The poem Sabse Khatarnak by the Hindi poet Pash was included in the NCERT textbook for 11th standard Hindi students in 2006. In 2017, the BJP government affiliated RSS tried to remove it but failed. [24] [25] The NCERT made two controversial changes to the class XII political science textbook ‘Politics in India Since Independence’ in 2017.
The version given here is that proven by Nash-Williams; Kruskal's formulation is somewhat stronger. All trees we consider are finite. Given a tree T with a root, and given vertices v, w, call w a successor of v if the unique path from the root to w contains v, and call w an immediate successor of v if additionally the path from v to w contains no other vertex.
Here are equivalent characterizations of real trees which can be used as definitions: 1) (similar to trees as graphs) A real tree is a geodesic metric space which contains no subset homeomorphic to a circle. [1] 2) A real tree is a connected metric space (,) which has the four points condition [2] (see figure):
The number of different binary trees on nodes is , the th Catalan number (assuming we view trees with identical structure as identical). For large n {\displaystyle n} , this is about 4 n {\displaystyle 4^{n}} ; thus we need at least about log 2 4 n = 2 n {\displaystyle \log _{2}4^{n}=2n} bits to encode it.
A B+ tree is an m-ary tree with a variable but often large number of children per node. A B+ tree consists of a root, internal nodes and leaves. [1] The root may be either a leaf or a node with two or more children.