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Mathematics Articles
Page 20 of 20
Complement of Graph
Let 'G−' be a simple graph with some vertices as that of 'G' and an edge {U, V} is present in 'G−', if the edge is not present in G. It means, two vertices are adjacent in 'G−' if the two vertices are not adjacent in G.If the edges that exist in graph I are absent in another graph II, and if both graph I and graph II are combined together to form a complete graph, then graph I and graph II are called complements of each other.ExampleIn the following example, graph-I has two edges 'cd' and 'bd'. Its complement ...
Read MoreCircuit Rank
Let 'G' be a connected graph with 'n' vertices and 'm' edges. A spanning tree 'T' of G contains (n-1) edges.Therefore, the number of edges you need to delete from 'G' in order to get a spanning tree = m-(n-1), which is called the circuit rank of G.This formula is true, because in a spanning tree you need to have 'n-1' edges. Out of 'm' edges, you need to keep 'n–1' edges in the graph.Hence, deleting 'n–1' edges from 'm' gives the edges to be removed from the graph in order to get a spanning tree, which should not form ...
Read MoreCenters of a tree
The center of a tree is a vertex with minimal eccentricity. The eccentricity of a vertex X in a tree G is the maximum distance between the vertex X and any other vertex of the tree. The maximum eccentricity is the tree diameter. If a tree has only one center, it is called Central Tree and if a tree has only more than one centers, it is called Bi-central Tree. Every tree is either central or bi-central.Algorithm to find centers and bi-centers of a treeStep 1 − Remove all the vertices of degree 1 from the given tree and also ...
Read MoreBipartite Graphs
Bipartite Graph - If the vertex-set of a graph G can be split into two disjoint sets, V1 and V2 , in such a way that each edge in the graph joins a vertex in V1 to a vertex in V2 , and there are no edges in G that connect two vertices in V1 or two vertices in V2 , then the graph G is called a bipartite graph.Complete Bipartite Graph - A complete bipartite graph is a bipartite graph in which each vertex in the first set is joined to every single vertex in the second set. The ...
Read MoreIndependent Line Set
Independent sets are represented in sets, in whichthere should not be any edges adjacent to each other. There should not be any common vertex between any two edges.there should not be any vertices adjacent to each other. There should not be any common edge between any two vertices.Independent Line SetLet 'G' = (V, E) be a graph. A subset L of E is called an independent line set of 'G' if no two edges in L are adjacent. Such a set is called an independent line set.ExampleLet us consider the following subsets −L1 = {a, b} L2 = {a, b} ...
Read MoreIndependent Vertex Set
Independent sets are represented in sets, in whichthere should not be any edges adjacent to each other. There should not be any common vertex between any two edges.there should not be any vertices adjacent to each other. There should not be any common edge between any two vertices.Independent Vertex SetLet 'G' = (V, E) be a graph. A subset of 'V' is called an independent set of 'G' if no two vertices in 'S' are adjacent.ExampleConsider the following subsets from the above graphs −S1 = {e} S2 = {e, f} S3 = {a, g, c} S4 = {e, d}Clearly, S1 ...
Read MoreWhy zero (0) is the first number?
Zero (0) is used as a number and also as the numerical digit. Zero gives the additive identity of the integers, real numbers, and many algebraic structures. It is used as a placeholder for writing numbers.Natural numbers start from 1, then 2 and so on. We cannot count backward with them. Integers, on the other hand, allows us to count backward. Zero winds up being a good choice for the number that should come after 1 as we count backward. Integers can go in both directions, to a positive infinity and also in the reverse direction to a negative infinity. ...
Read MoreArithmetic of Number Systems\\n
A number system is a set of symbols used to represent values derived from a common base or radix. In a number, the value of each digit can be determined using digit, position of the digit in the number, and the base of the number system. The base is defined as the total number of digits are available in the number system. This is known as positional number system.Number SystemBaseDigit UsedBinary20, 1Octal80, 1, 2, 3, 4, 5, 6, 7Decimal100, 1, 2, 3, 4, 5, 6, 7, 8, 9Hexadecimal160, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, ...
Read MoreNegative Binary Numbers\\n
Negative numbers can be distinguishable with the help of extra bit or flag called sign bit or sign flag in Binary number representation system for signed numbers. It is not possible to add minus or plus symbol in front of a binary number because a binary number can have only two symbol either 0 or 1 for each position or bit. That’s why we use this extra bit called sign bit or sign flag. The value of sign bit is 1 for negative binary numbers and 0 for positive numbers.When an integer binary number is positive, the sign is represented ...
Read MoreWhat is Vernier Calipers and How it is used for Measurement?
Measuring things and distances is one of the important concepts to learn when we are studying maths. For maximum uses, measuring scales do the work quite well and everyone is aware of it how to use one. But the measuring scale only provides a specific level of correctness and once you need exact measurements which lie between two spots on the scale it becomes difficult to get a correct reading without a bit of counterpart.Also measuring scales are very vulnerable to parallax mistakes which can cause a huge portion of the difference in readings from person to person which is ...
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