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Showing posts with the label BSc-III

How to find the incidence matrix . (graph Theory )

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how to  Find the incidence matrix for the following graph What is the Incidence Matrix, Example of an incident matrix? B.Sc III [Semester - VI (Paper-XII) Graph Theory  Matrix Representation of Graph 

A connected graph G is an Euler graph iff every vertex of ‘G’ is of even degree.

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B.Sc III [ Semester -VI ( Paper-XII) ] Graph Theory 

Prove that any two simple connected graph with ‘n’vertices all of degree two are isomorphic.

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B.Sc III [ Semester -VI ( Paper-XII) ] Graph Theory 

A connected graph G is an Euler graph iff it can be decomposed into circuit .

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B.Sc III [Semester - VI (Paper-XII) Graph Theory 

Operation on Graphs

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B.Sc III [Semester - VI (Paper-XII) Graph Theory      Operation on Graphs :- 

Let G1 and G2 be any two graphs then Union , Intersection and ring sum of these graphs as shown below G1∪ G2 , G1∩ G2 , G1 + G2

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B.Sc III [Semester - VI (Paper-XII) Graph Theory 

Using Gram-Schmidt orthogonalisation process, orthonormalise the LI subset { (1,1,1) , (0,1,1) , (0,0,1) } of V3 .

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  B.Sc III - [ Semester - VI (Paper-XI ) ] Unit - 4 Inner product spaces  Gram-Schmidt orthogonal process example

Show that the orthogonal complement of w is a subspace of v.

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B.Sc III [Semester VI  (Paper-XI) ] Unit - 4  Inner product spaces 

If a is a generator of a cyclic group G, then a-1 is also a generator of G.

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B.Sc. II [ Semester - IV (Paper - VII ) Unit - 1   [Some special groups ]

Let a be the generator of a cyclic group G such that o (a) = n . Then For m ∈ Z , am = e  m ≡ 0 (mod n ) In general , ar = as  r ≡ s (modn ) for r , s ∈ Z .

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B.Sc II [ Semester  IV (Paper - VII ) Unit - 1   [Some special groups ] Order of a generator of a cyclic group :- 

Konigsberg Bridge Problem

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Konigsberg Bridge Problem :-                                    In the eighteenth century good citizens of Konigsberg, capital of   Eastern Prussia (   now renamed kalningrad and in West Soviet Russia ) would amuse themselves with the following puzzle. Through the city flowed the lovely river Pregel, formed two islands C, D ( C is kneiphof island   ) were connected to each other and to the banks A and B with seven Bridges (known as Green, merchant’s, Blacksmith’s High, wooden, connecting and Hone as shown in fig. (a).                           The problem was to start at any of the four land areas of city, A, B, C or D, walk   over   each   of   the ...

Show whether the following graphs are isomorphic or not.

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B.Sc III [ Semester -VI ( Paper-XII) ] Graph Theory 

Draw the graph of the Wheatstone bridge circuit.

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B.Sc. III year all topics

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B.Sc. III year Semester - VI - (Paper-XII) [ Graph Theory ] Unit - 1 ( Introduction to Graphs ) Click here 👉   1)   All definitions of graph theory paper. Click here 👉   2)   Handshaking lemma Theorem. Click here 👉   3) Draw all simple graphs of one, two three and four vertices . Click here 👉   4) Draw the graph of the following chemical compound.                               (1) CH 4       (2) C 2 H 6       (3) C 6 H 12        (4) N 2 O 3   Click here 👉 5) Draw the graph of the Wheatstone bridge circuit.   Click here 👉  6)  Konigsberg Bridge Problem Click here 👇 7 )  Click here 👇 ( 8)    Prove that a simple graph having n vertices and k co...

Draw the graph of following chemical compound : (1) CH4 (2) C2H6 (3) C6H12 (4) N2O3

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B.Sc III [ Semester -VI ( Paper-XII) ] Graph Theory  ================================================================ Click onit  to view this 👇 Draw the graph of the Wheatstone bridge circuit

Draw all simple graph of one , two , three and four vertices.

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B.Sc III [ Semester -VI ( Paper-XII) ] Graph Theory