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A graph is traversable if you can draw a path between all the vertices without retracing the same path. Based on this path, there are some categories like Euler’s path and Euler’s circuit which are described in this chapter.Euler’s PathAn Euler’s path contains each edge of ‘G’ exactly once and each vertex of ‘G’ at least once. A connected graph G is said to be traversable if it contains an Euler’s path.ExampleEuler’s Path = d-c-a-b-d-e.Euler’s CircuitIn an Euler’s path, if the starting vertex is same as its ending vertex, then it is called an Euler’s circuit.ExampleEuler’s Path = a-b-c-d-a-g-f-e-c-a.Euler’s Circuit ... Read More
For this, you can use time_format() and time_diff(). To find the time difference, you need to use the time_diff() method. Let us first create a table −mysql> create table DemoTable624 (PunchIn datetime, PunchOut datetime); Query OK, 0 rows affected (0.60 sec)Insert some records in the table using insert command −mysql> insert into DemoTable624 values('2019-07-14 12:10:00', '2019-07-14 12:50:00'); Query OK, 1 row affected (0.12 sec) mysql> insert into DemoTable624 values('2019-07-14 11:00:00', '2019-07-14 11:30:00'); Query OK, 1 row affected (0.34 sec)Display all records from the table using select statement −mysql> select *from DemoTable624;This will produce the following output −+---------------------+---------------------+ | PunchIn ... Read More
A graph is a set of points, called nodes or vertices, which are interconnected by a set of lines called edges. The study of graphs, or graph theory is an important part of a number of disciplines in the fields of mathematics, engineering and computer science.Graph TheoryDefinition − A graph (denoted as G = (V, E)) consists of a non-empty set of vertices or nodes V and a set of edges E. A vertex a represents an endpoint of an edge. An edge joins two vertices a, b and is represented by set of vertices it connects.Example − Let us ... Read More
Let us first create a table −mysql> create table DemoTable623 (FirstName varchar(100), LastName varchar(100), Age int); Query OK, 0 rows affected (0.76 sec)Insert some records in the table using insert command −mysql> insert into DemoTable623 values('John', 'Smith', 23); Query OK, 1 row affected (0.66 sec) mysql> insert into DemoTable623 values('Adam', 'smith', 23); Query OK, 1 row affected (0.26 sec) mysql> insert into DemoTable623 values('Chris', 'Brown', 24); Query OK, 1 row affected (0.11 sec) mysql> insert into DemoTable623 values('Robert', 'brown', 21); Query OK, 1 row affected (0.22 sec)Display all records from the table using select statement −mysql> select *from DemoTable623;This will ... Read More
Distance between Two VerticesIt is number of edges in a shortest path between Vertex U and Vertex V. If there are multiple paths connecting two vertices, then the shortest path is considered as the distance between the two vertices.Notation − d(U, V)There can be any number of paths present from one vertex to other. Among those, you need to choose only the shortest one.ExampleTake a look at the following graph −Here, the distance from vertex 'd' to vertex 'e' or simply 'de' is 1 as there is one edge between them. There are many paths from vertex 'd' to vertex ... Read More
Let us first create a table −mysql> create table DemoTable622 (Id int NOT NULL AUTO_INCREMENT PRIMARY KEY, Value1 int, Value2 int); Query OK, 0 rows affected (1.08 sec)Insert some records in the table using insert command −mysql> insert into DemoTable622(Value1, Value2) values(1000, 1000); Query OK, 1 row affected (0.23 sec) mysql> insert into DemoTable622(Value1, Value2) values(2000, 3000); Query OK, 1 row affected (1.04 sec)Display all records from the table using select statement −mysql> select *from DemoTable622;This will produce the following output −+----+--------+--------+ | Id | Value1 | Value2 | +----+--------+--------+ | 1 | 1000 | 1000 ... Read More
Let us first create a table −mysql> create table DemoTable621 (UserName varchar(100), UserEmailId varchar(100), UserLastPost datetime); Query OK, 0 rows affected (0.59 sec)Insert some records in the table using insert command −mysql> insert into DemoTable621 values('John', 'John@gmail.com', '2019-04-10 11:01:10'); Query OK, 1 row affected (0.47 sec) mysql> insert into DemoTable621 values('John', 'John@gmail.com', '2019-07-14 13:07:10'); Query OK, 1 row affected (0.15 sec)Display all records from the table using select statement −mysql> select *from DemoTable621;This will produce the following output −+----------+----------------+---------------------+ | UserName | UserEmailId | UserLastPost | +----------+----------------+---------------------+ | John | ... Read More
Whether it is possible to traverse a graph from one vertex to another is determined by how a graph is connected. Connectivity is a basic concept in Graph Theory. Connectivity defines whether a graph is connected or disconnected. It has subtopics based on edge and vertex, known as edge connectivity and vertex connectivity. Let us discuss them in detail.ConnectivityA graph is said to be connected if there is a path between every pair of vertex. From every vertex to any other vertex, there should be some path to traverse. That is called the connectivity of a graph. A graph with ... Read More
Connected GraphA graph is connected if any two vertices of the graph are connected by a path.Vertex 1Vertex 2PATHaba baca b c, a cada b c d, a c dbcb a c , b ccdc dDisconnected GraphA graph is disconnected if at least two vertices of the graph are not connected by a path. If a graph G is disconnected, then every maximal connected subgraph of G is called a connected component of the graph G.Vertex 1Vertex 2PATHaba bacNot AvailableadNot AvailablebcNot Availablecdc d
Trees are graphs that do not contain even a single cycle. They represent hierarchical structure in a graphical form. Trees belong to the simplest class of graphs. Despite their simplicity, they have a rich structure.Trees provide a range of useful applications as simple as a family tree to as complex as trees in data structures of computer science.TreeA connected acyclic graph is called a tree. In other words, a connected graph with no cycles is called a tree.The edges of a tree are known as branches. Elements of trees are called their nodes. The nodes without child nodes are called ... Read More