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Articles by Mahesh Parahar
Page 14 of 14
Circuit 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 ...
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