MCA Articles - Page 73 of 102

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 More

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 More

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 More

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 More

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 More

Throughput of a system refers to the rate of processing of a task thereby generating results. Ethernet is a set of technologies primarily used in LANs, whose primary data units are frames. The throughput of Ethernet is measured by the rate of successful delivery of frames over a communication channel.There are several methods for representing Ethernet throughput. The least ambiguous among them is calculation of channel efficiency. Channel efficiency, is the percentage of the net bit rate (in bits per second) of a channel that is actually communicated. Suppose that an Ethernet connection has a speed of 100 Mbps. But, ... Read More

Carrier Sense Multiple Access with Collision Detection (CSMA/CD) is a network protocol for carrier transmission that operates in the Medium Access Control (MAC) layer. It senses or listens whether the shared channel for transmission is busy or not, and defers transmissions until the channel is free.When more than one stations send their frames simultaneously, collision occurs. Back-off algorithm is a collision resolution mechanism which is commonly used to schedule retransmissions after collisions in Ethernet. The waiting time that a station waits before attempting retransmission of the frame is called as back off time.Algorithm of CSMA/CDStep 1) When a frame is ... Read More

100BASE-T4 is the early implementation of Fast Ethernet over twisted pair cables, carrying data traffic at 100 Mbps (Mega bits per second) in local area networks (LAN). It was launched as the IEEE 802.3u standard in 1995. Here, 100 is the maximum throughput, i.e. 100 Mbps, BASE denoted use of baseband transmission, and T4 denotes use of four twisted pair cables in Fast Ethernet.PropertiesThis has four pairs of unshielded twisted pair of Category 3. i.e. voice grade.Two of these pairs are bi-directional and the other two are unidirectional. The two unidirectional wires are reserved for receiving and sending data respectively. ... Read More

100BASE-FX is the technical name of Fast Ethernet over fiber optic cables. It is a version of Fast Ethernet carrying data traffic at 100 Mbps (Mega bits per second) in local area networks (LAN). It was launched as the IEEE 802.3u standard in 1995. Here, 100 is the maximum throughput, i.e. 100 Mbps, BASE denoted use of baseband transmission, and FX denotes use of optical fibers in Fast Ethernet.The 100BASE-FX Physical Medium Dependent (PMD) sublayer is defined by Fiber Distributed Data Interface (FDDI).PropertiesThis has two pairs of optical fibers. One pair transmits frames from hub to the device and the ... Read More

100BASE-TX is the technical name of Fast Ethernet over twisted pair cables. It is a predominant form of Fast Ethernet carrying data traffic at 100 Mbps (Mega bits per second) in local area networks (LAN). It was launched as the IEEE 802.3u standard in 1995. Here, 100 is the maximum throughput, i.e. 100 Mbps, BASE denoted use of baseband transmission, and TX denotes use of twisted pair cables in Fast Ethernet.PropertiesThis has either two pairs of unshielded twisted pairs (UTP) category 5 wires or two shielded twisted pairs (STP) type 1 wires.One of these pairs transmits frames from hub to ... Read More