definition of walk in graph theory with examples
Path (graph theory) A path is a trail in which all vertices (except possibly the first and last) are distinct. A trail is a walk in which all edges are distinct. A walk of length   k  {\displaystyle k}  in a graph is an alternating sequence of vertices and edges,   v 0  , e 0  , v 1  , e 1  , v 2  , … , v k − 1  , e k − 1  , v k   {\displaystyle v_{0},e_{0},v_{1},e_{1},v_{2},\ldots ,v_{k-1},e_{k-1},v_{k}} , which begins and ends with vertices. If the graph is undirected, then the endpoints of   e i   {\displaystyle e_{i}}  are   v i   {\displaystyle v_{i}}  and   v i + 1   {\displaystyle v_{i+1}} . If the graph is directed, then   e i   {\displaystyle e_{i}}  is an arc from   v i   {\displaystyle v_{i}}  to   v i + 1   {\displaystyle v_{i+1}} . An infinite path is an alternating sequence of the same type described here, but with no first or last vertex, and a semi-infinite path (also ray) has a first vertex,   v 0   {\displaystyle v_{0}} , but no last vertex. Most authors require that all of the edges and vertices be distinct from one another. However, some authors do not make this requirement, and instead use the term simple path to refer to a path which contains no repeated vertices.
List of districts in India A district (
Algorithm As an effective method, an algorithm can be expressed within a finite amount of space and time[1] and in a well-defined formal language[2] for calculating a function.[3] Starting from an initial state and initial input (perhaps empty),[4] the instructions describe a computation that, when executed, proceeds through a finite[5] number of well-defined successive states, eventually producing "output"[6] and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.[7]
Mean value theorem This theorem is used to prove statements about a function on an interval starting from local hypotheses about derivatives at points of the interval.