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What is a biclique?

A biclique is a term used in graph theory for a special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set.


Can a graph have a euler circuit but not a hamiltonian circuit?

Yes. Example: .................................................... ...A * ........................................... ......|.\ ......................................... eg Euler circuit: ACDCBA ......|...\ ........... --------- ............. ......|.....\........./...............\............ The Hamilton circuit is impossible as it has two ......|.......\...../...................\.......... halves (ACD & CD) connected to each other only ......|.........\./.......................\........ at vertex C. Once vertex C has been reached in ......|.......C *........................* D.... one half, it can only be used to start a path in ......|........./.\......................./......... the other half, or complete the cycle in the ......|......./.....\.................../........... current half; or if the path starts at C, it will end ......|...../.........\.............../............. without the other half being visited before C is ......|.../ ........... --------- .............. revisited. ......|./ ........................................... ...B *.............................................. ......................................................


Define walk path and connected graph in an algorithm?

A "walk" is a sequence of alternating vertices and edges, starting with a vertex and ending with a vertex with any number of revisiting vertices and retracing of edges. If a walk has the restriction of no repetition of vertices and no edge is retraced it is called a "path". If there is a walk to every vertex from any other vertex of the graph then it is called a "connected" graph.


What is a hamiltonian path in a graph?

A Hamiltonian path in a graph is a path that visits every vertex exactly once. It does not need to visit every edge, only every vertex. If a Hamiltonian path exists in a graph, the graph is called a Hamiltonian graph.


Is every resistance load resistance?

No. Load resistance is the value of the element actually doing the work of the circuit it is connected to. A speaker connected to an amplifier is the load.


Does every angle have a vertex?

Every angle has a vertex. A vertex is simply the line through the center of each angle. The line splits the angle exactly in half.


What is a motherboard for?

that is the main circuit board inside a computer. Every other component is connected to the motherboard in order to work.


What is krushkal algorithm?

Kruskal's algorithm is an algorithm in graph theory that finds a minimum spanning tree for a connected weighted graph. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized. If the graph is not connected, then it finds a minimum spanning forest (a minimum spanning tree for each connected component). Kruskal's algorithm is an example of a greedy algorithm.


What is a rule for current flowing round a circuit?

In a series circuit, the current at every point in the circuit is the same. This is a consequence of Kirchoff's Current Law, which states that the signed sum of the currents entering a node must equal zero. Since a series circuit consists of nodes with only two elements connected to each node, it follows that the current at every point in a series circuit is the same.


What do Kirchhoff's voltage law mean?

Both of Kirchhoff's laws are simple conservation laws:Kirchhoff's voltage law means that voltage must be conserved around every loop in a circuit, no voltage can be gained or lost by traversing a loop, which is usually stated as the sum of the voltages around a loop (for every loop in the circuit) must be zero.Kirchhoff's current law means that current must be conserved at every node in a circuit, no current can be gained or lost by any branch connected to a node, which is usually stated as the sum of the currents in all branches connected to a node (for every node in the circuit) must be zero.


Is An apothem is drawn from the center of a polygon to every vertex?

No.


Prove that every tree with two or more vertices is bichromatic?

Prove that the maximum vertex connectivity one can achieve with a graph G on n. 01. Define a bipartite graph. Prove that a graph is bipartite if and only if it contains no circuit of odd lengths. Define a cut-vertex. Prove that every connected graph with three or more vertices has at least two vertices that are not cut vertices. Prove that a connected planar graph with n vertices and e edges has e - n + 2 regions. 02. 03. 04. Define Euler graph. Prove that a connected graph G is an Euler graph if and only if all vertices of G are of even degree. Prove that every tree with two or more vertices is 2-chromatic. 05. 06. 07. Draw the two Kuratowski's graphs and state the properties common to these graphs. Define a Tree and prove that there is a unique path between every pair of vertices in a tree. If B is a circuit matrix of a connected graph G with e edge arid n vertices, prove that rank of B=e-n+1. 08. 09.