Eular
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.
No.
Yes.
True.
It is traversable if there is an even number of edges at each vertex, or at every vertex except two. In the latter case the traverse must start at one of the "odd vertices" and finish at the other.
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.
Yes, a graph can have an Euler circuit (a circuit that visits every edge exactly once) but not have a Hamiltonian circuit (a circuit that visits every vertex exactly once). This can happen when the graph has certain degree requirements that allow for the Euler circuit but prevent the existence of a Hamiltonian circuit.
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.
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.
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.
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.
that is the main circuit board inside a computer. Every other component is connected to the motherboard in order to work.
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.
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.
No.
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.
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.