Plane Graph in a sentence
(1) In a plane graph, each edge connects two vertices.
(2) A plane graph can have multiple connected components.
(3) A plane graph can have any number of vertices and edges.
(4) The concept of a plane graph is important in graph theory.
(5) In a plane graph, each vertex represents a point on the plane.
(6) The concept of a plane graph is widely used in network analysis.
(7) A plane graph can be used to solve various optimization problems.
(8) The concept of a plane graph is closely related to planar graphs.
(9) The vertices of a plane graph are represented by points on the plane.
(10) The properties of a plane graph can be studied using graph algorithms.
Plane Graph sentence
(11) A plane graph can be used to analyze the connectivity of a power grid.
(12) A plane graph can be used to model the layout of a city's road network.
(13) A plane graph can be used to analyze the structure of a social network.
(14) A plane graph can have multiple edges between the same pair of vertices.
(15) A plane graph can be used to represent a network of interconnected nodes.
(16) In a plane graph, the length of a path is the number of edges in the path.
(17) The edges of a plane graph are represented by straight lines on the plane.
(18) A plane graph can be used to model the layout of a transportation network.
(19) The concept of a plane graph is fundamental in understanding graph theory.
(20) A plane graph can have multiple edges connecting the same pair of vertices.
Plane Graph make sentence
(21) The concept of a plane graph is applicable in various real-world scenarios.
(22) A plane graph can be used to represent the layout of a city's road network.
(23) The concept of a plane graph is often used in solving optimization problems.
(24) In a plane graph, the length of a cycle is the number of edges in the cycle.
(25) A plane graph can be used to analyze the connectivity of a computer network.
(26) The Euler's formula is often used to analyze the properties of a plane graph.
(27) The concept of a plane graph is also applicable in the field of circuit design.
(28) In a plane graph, the degree of a vertex is the number of edges incident to it.
(29) The concept of a plane graph is often used in computer science and mathematics.
(30) The concept of a plane graph is closely related to the concept of planar graphs.
Sentence of plane graph
(31) A plane graph is a graph that can be drawn on a plane without any edges crossing.
(32) In a plane graph, the face-degree of a face is the number of edges incident to it.
(33) The properties of a plane graph can be used to solve complex optimization problems.
(34) The properties of a plane graph can be used to analyze the complexity of a problem.
(35) The concept of a plane graph is widely used in computer science and network analysis.
(36) The concept of a plane graph is useful in solving problems related to graph coloring.
(37) A plane graph can be used to represent the flow of information in a computer network.
(38) A plane graph can be used to visualize the connections between different data points.
(39) The edges in a plane graph connect the vertices and can be represented as straight lines.
(40) The concept of a plane graph is widely used in graph algorithms and optimization problems.
Plane Graph meaningful sentence
(41) A plane graph can be used to represent the flow of information in a communication network.
(42) The concept of a plane graph is essential in studying the topological properties of graphs.
(43) A plane graph can be used to model the connections between different components in a system.
(44) A plane graph can be used to represent the dependencies between different tasks in a project.
(45) The concept of a plane graph is fundamental in understanding the properties of planar graphs.
(46) In a plane graph, the sum of the degrees of all vertices is equal to twice the number of edges.
(47) A plane graph can have multiple cycles, with each cycle representing a closed loop in the graph.
(48) A plane graph can have multiple faces, with the outer face representing the exterior of the graph.
(49) A plane graph can be used to represent the interactions between different species in an ecosystem.
(50) The properties of a plane graph can be used to optimize the efficiency of a transportation system.
Plane Graph sentence examples
(51) A plane graph can be used to represent the connections between different neurons in a neural network.
(52) The dual of a plane graph is another plane graph obtained by swapping the roles of vertices and faces.
(53) A plane graph can be used to represent the connections between different computer systems in a network.
(54) The number of edges in a plane graph is always less than or equal to three times the number of vertices.
(55) The concept of a plane graph is applicable in various fields, including computer science and mathematics.
(56) A plane graph can be used to represent the connections between different nodes in a communication network.
(57) A plane graph can be used to represent the interactions between different species in an ecological network.
(58) A plane graph can be used to represent the connections between different electronic components in a circuit.
(59) The concept of a plane graph is crucial in understanding the dynamics of information propagation in a network.
(60) A plane graph can be used to represent the connections between different power stations in an electrical grid.
Sentence with plane graph
(61) The concept of a plane graph is also relevant in analyzing the relationships between individuals in a social network.
(62) The concept of a plane graph is fundamental in understanding the topological properties of different graph structures.
(63) The concept of a plane graph is often used in analyzing the efficiency and robustness of different network structures.
(64) The concept of a plane graph is essential in understanding the connectivity and reachability of different network nodes.
(65) A plane graph can have multiple spanning trees, with each spanning tree representing a subset of edges that form a tree.
(66) A plane graph can be used to represent a map of a city, with each vertex representing a location and each edge representing a road.
(67) A plane graph can have multiple planar embeddings, with each embedding representing a different way of drawing the graph on a plane.
(68) A plane graph can have multiple Hamiltonian cycles, with each Hamiltonian cycle representing a cycle that visits each vertex exactly once.
(69) A plane graph can be used to represent the layout of a circuit, with each vertex representing a component and each edge representing a connection.
Plane Graph meaning
Plane graph is a term commonly used in mathematics and graph theory to describe a graph that can be embedded in a plane without any edges crossing each other. It is a fundamental concept in the field and has various applications in different areas of study. In this article, we will explore tips on how to use the phrase "plane graph" effectively in sentences.
1. Definition and Explanation: When introducing the term "plane graph" in a sentence, it is essential to provide a clear and concise definition.
For example, "A plane graph is a graph that can be drawn on a plane without any edges crossing." This initial explanation helps establish the context for further discussion.
2. Contextual Examples: To illustrate the concept of a plane graph, it is helpful to provide examples in sentences. For instance, "The map of a city can be represented as a plane graph, where the streets are edges, and the intersections are vertices." This example demonstrates how the term can be applied in a real-world scenario.
3. Graph Theory Applications: To showcase the significance of plane graphs in graph theory, it is beneficial to mention their applications. For instance, "Plane graphs are extensively used in network routing algorithms, as they provide a visual representation of connections between nodes." This highlights the practical implications of the term and its relevance in various fields.
4. Properties and Characteristics: When discussing plane graphs, it is important to mention their properties and characteristics.
For example, "One notable property of a plane graph is that it divides the plane into regions called faces." This statement emphasizes a key feature of plane graphs and helps deepen the understanding of the term.
5. Relationship with Other Graphs: To provide a comprehensive understanding of plane graphs, it can be helpful to discuss their relationship with other types of graphs. For instance, "A planar graph is a graph that can be drawn on a plane without any edges crossing, whereas a non-planar graph cannot be represented as a plane graph." This comparison highlights the distinction between plane graphs and other graph types.
6. Historical Background: Including a brief historical background can add depth to the discussion of plane graphs.
For example, "The concept of plane graphs was first introduced by the Swiss mathematician Leonhard Euler in the 18th century." This historical context acknowledges the origins of the term and the contributions of notable mathematicians.
7. Practical Usage: To demonstrate the practical usage of the term "plane graph," it can be helpful to provide examples from different fields. For instance, "In computer graphics, plane graphs are used to represent the connectivity of polygons in 3D models." This example showcases how the term is applied in a specific industry or discipline.
8. Further Exploration: To encourage further exploration of the topic, it is beneficial to suggest additional resources or references.
For example, "For a more in-depth understanding of plane graphs, one can refer to textbooks on graph theory or academic papers on the subject." This provides readers with avenues to delve deeper into the concept if they wish to expand their knowledge.
In conclusion, the term "plane graph" is a fundamental concept in mathematics and graph theory. By following these tips, you can effectively incorporate the phrase into sentences, providing a clear understanding of its definition, applications, properties, and historical background.
The word usage examples above have been gathered from various sources to reflect current and historical usage of the word Plane Graph. They do not represent the opinions of TranslateEN.com.