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Chromatic Polynomial of a Graph || Polynomial in Graph Theory || Chromatic Number
The chromatic polynomial of graph G is a polynomial function which defines how many ways we can color a graph with some number of colors. So we can write chromatic polynomial of a graph of n vertices denoted by f(G,λ), where we have λ number of colors.
Просмотров: 5 030
Видео
Thickness and Crossing
Просмотров 3106 месяцев назад
The Thickness of a graph G is the minimum number of planar graphs into which the edges of G can be partitioned. That is, if there exists a collection of k planar graphs, all having the same set of vertices, such that the union of these planar graphs is G, then the thickness of G is at most k. The crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the...
Matching and Covering
Просмотров 1,3 тыс.6 месяцев назад
A vertex is matched (or saturated) if it is an endpoint of one of the edges in the matching. Otherwise the vertex is unmatched (or unsaturated). A maximal matching is a matching M of a graph G that is not a subset of any other matching. A matching M of a graph G is maximal if every edge in G has a non-empty intersection with at least one edge in M. The following figure shows examples of maximal...
Chromatic Partitioning || Chromatic partitioning in Graph Theory
Просмотров 2,8 тыс.6 месяцев назад
Chromatic partitioning is a process of dividing a graph into a minimum number of disjoint subsets such that each subset is an independent set. An independent set is a set of vertices in a graph such that no two vertices are adjacent.
Graph Coloring and Chromatic Number || Coloring of a Graph || Chromatic Number
Просмотров 3786 месяцев назад
A graph coloring is an assignment of labels, called colors, to the vertices of a graph such that no two adjacent vertices share the same color. The chromatic number χ(G) of a graph G is the minimal number of colors for which such an assignment is possible. The chromatic number of a graph G, denoted as χ(G), is the minimum number of colors required to color the vertices of a graph G in such a wa...
Combinatorial Dual || Dual in Graph Theory
Просмотров 8376 месяцев назад
A graph G∗ is said to be a combinatorial dual (sometimes also called algebraic dual) of another graph G if there is a bijection between their edges such that the polygons of one of them correspond to the cut-sets of the other, and vice versa. A graph can have no combinatorial duals, or it can have multiple non-isomorphic combinatorial duals.
Geomatric Dual of a Graph
Просмотров 3836 месяцев назад
A geometric dual of a graph is formed by embedding that graph in the plane (taking a set of points for the vertices and curves with non-intersecting interiors between them for the edges), assigning to each face (connected component of the complement of the embedding) a vertex as a point in the face, and connecting vertices with an edge passing through the edge connecting their faces (and inters...
Detection of Planarity of a Graph || Graph Theory || Planar Graph
Просмотров 6056 месяцев назад
Detection of Planarity of a Graph || Graph Theory || Planar Graph
Planar Graph || Kuratowski's Theorem of Non-planar Graph || Kuratowski's two non-planar graph
Просмотров 5426 месяцев назад
A Planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. A complete graph with five vertices is the first of the two graphs of Kuratowski. The second graph of Kuratowski is a regular connected graph with six vertices...
Relationship among Af, Bf and Cf matrices of a Graph
Просмотров 3396 месяцев назад
1. Reduced Incidence Matrix can be written as Af = | Ac | At | 2. Fundamental Circuit Matrix can be written as Bf = | Iμ | Bt | 3. Fundamental Cut-set Matrix can be written as Cf = | Cc | Iμ-1 | Relationship among them can be expressed through the following expression as an outcome: At-1. Ac = BtT = Cc
Reduced Incidence Matrix (Af) of a Graph || Matrices in Graph Theory
Просмотров 1166 месяцев назад
It is another form of incidence matrix A, from which a row (consisting 0 and 1 as a relation with edges) is removed for some specific purposes. It is generally denoted by Af.
Incidence Matrix of Directed and Undirected Graph
Просмотров 966 месяцев назад
The incidence matrix A of an undirected graph has a row for each vertex and a column for each edge of the graph. The element A[[i,j]] of A is 1 if the ith vertex is a vertex of the jth edge and 0 otherwise. The incidence matrix A of a directed graph has a row for each vertex and a column for each edge of the graph.
Fundamental Cutset Matrix (Cf) || Matrix in Graph Theory
Просмотров 1316 месяцев назад
Fundamental Cut-set Matrix. Fundamental cut set or f-cut set is the minimum number of branches that are removed from a graph in such a way that the original graph will become two isolated subgraphs. The f-cut set contains only one twig and one or more links.
Fundamental Circuit Matrix (Bf) || Matrix in Graph Theory
Просмотров 2026 месяцев назад
To determine the fundamental circuits in a graph, we can use the following steps: Select a spanning tree (a tree that spans all the vertices in the graph). For each edge that is not in the tree [ i.e. chord set ], add it to the tree to form a fundamental circuit. For all the chords we get a fundamental circuit.
Adjanceny Matrix of Directed and Undirected Graph || Matrix in Graph Theory
Просмотров 1076 месяцев назад
An adjacency matrix is a square matrix of N x N size where N is the number of nodes in the graph and it is used to represent the connections between the edges of a graph. Characteristics of the adjacency matrix are: The size of the matrix is determined by the number of vertices in the graph. The number of nodes in the graph determines the size of the matrix. The number of edges in the graph is ...
Characterisitic & Excitation table of T Flip-Flop | Characterisitic, Excitation table of D Flip-Flop
Просмотров 279 месяцев назад
Characterisitic & Excitation table of T Flip-Flop | Characterisitic, Excitation table of D Flip-Flop
Characterstic and Excitation table of JK Flip-Flop | Excitation Table of JK Flip-Flop|
Просмотров 149 месяцев назад
Characterstic and Excitation table of JK Flip-Flop | Excitation Table of JK Flip-Flop|
Excitation table of SR Flip-Flop | Characteristics Table and Equation of SR Flip-Flop
Просмотров 419 месяцев назад
Excitation table of SR Flip-Flop | Characteristics Table and Equation of SR Flip-Flop
D Flip-Flop Design using NOR Gate | D Flip-Flop by NOR in Hindi | Sequential Circuit Design
Просмотров 1 тыс.9 месяцев назад
D Flip-Flop Design using NOR Gate | D Flip-Flop by NOR in Hindi | Sequential Circuit Design
D Flip-Flop design using NAND Gate | D Flip-Flop in Hindi | Sequential Circuit Design |
Просмотров 659 месяцев назад
D Flip-Flop design using NAND Gate | D Flip-Flop in Hindi | Sequential Circuit Design |
T Flip-Flip Design using NOR Gate || T Flip-Flop || Sequential Circuit design || Flip-Flop in Hindi
Просмотров 409 месяцев назад
T Flip-Flip Design using NOR Gate || T Flip-Flop || Sequential Circuit design || Flip-Flop in Hindi
T Flip-Flip Design using NAND Gate || Flip-Flop Design || Toggle Flipflop
Просмотров 529 месяцев назад
T Flip-Flip Design using NAND Gate || Flip-Flop Design || Toggle Flipflop
Introduction to Flipflops and Its Types
Просмотров 259 месяцев назад
Introduction to Flipflops and Its Types
Spanning Tree | Rank and Nullity of a Graph | Branch and Chord of a Graph
Просмотров 1899 месяцев назад
Spanning Tree | Rank and Nullity of a Graph | Branch and Chord of a Graph
Graph Operations-Part5 | Composition of Two Graphs | Lexicographic Product of Two Graphs |
Просмотров 1859 месяцев назад
Graph Operations-Part5 | Composition of Two Graphs | Lexicographic Product of Two Graphs |
Graph Operations-Part-4| Product of Two Graphs
Просмотров 2569 месяцев назад
Graph Operations-Part-4| Product of Two Graphs
Thnk u sir for the nice explanation
Thanku
Gazab explanation sir
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thank u so much sir
Thanku
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Only 1 fundamental circuit nhi hoga?
We have to take orientation mean direction
best
Thank you sir❤
Most welcome
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God bless u
Very nice video sir, Thank you so much.
thanku so much...please subscribe from other devices too.
Wont 2,4,5 be also a fundamental ckt
Yes it is..even at 6:44 time i mentioned it clearly..thanku
Thnx sir
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18 th example sum
Good evening sir🙇🏻♀️🙏🏻 Sir jaise isme ek subset aur bn rha S = (B, C, D)... To agr hm isme se D ko hta de... To graph mein difference aayega... To ye subset S = ( B, C, D) minimal vertex set mein aayega n?
Yes ofcourse...beacuse removal of D will leave edge 4 uncovered..
@mushi172 Thank you sir 🙏🏻☺️
Badiya sir 😊
Thank you Sir. Apka voice thorasa kam ay raha hain.
clear explaination sir!
Glad you liked it
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Watched so many videos on this topic, none explained it like you did sir! Thank you.
Glad it was helpful!
@@mushi172 bhakk
best lecture on youtube for this topic
Thanku
ab chhupa bhi maarle uska
First of all ....All the best for u youtube and you r explaining amazing way
Thank you so much 😀
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Very Nice Explanation Sir.....Subscribed and liked many videos...Keep making sir...and also u have very very good handwriting sir
Watching from NIT Srinagar [CSE].Today is my exam.Thank You Sir.
All the best
thank youu
Thanku
K4 is a planar graph with highest number of vertices
New and fruitful channel for maths, thanks a lot sir, you cover all the portions as well as every aspect of a problem, which is great❤ A great channel specially for the students of MAKAUT
Thanku so much..kindly share with your friends and students. Do subscribe please
@@mushi172sure
Thanks sir 😊
Most welcome
well explained thank you keep it up🙂
Most welcome 😊
Good explanation sir
Thanks and welcome
Thank You sir ji
All the best
Thanks Sir ji
THANKS A LOT SIR
THANKS A LOT SIR
thankue sir ji
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Thank you sir
Welcome
Aap kaha se ho bhaiya
Mai Dehradun se hu..ap batao
Thank you sir ji
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Kya matlab sab ke sab abhi hi video dekhne baithe hain😂
Thankue sir ji
❤
Wonderful explanation sir
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Thank for sharing Playlist sir 🙏
Most welcome
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Nice explanation sir🙏
Thankyou
Thank you,
Very useful
Great explanation sir👍