Gargi Vadalia
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- Joined
- Jun 5, 2024
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Question-
Consider the following degree sequence: {7, 7, 5, 5, 5, 3, 2, 2}.
(a) Is it possible to sketch a simple graph that has this degree
sequence? If yes, sketch the graph. If not, give a convincing argument why it is not
possible.
We recommend to first establish the number of vertices and edges of such a graph, if it
exists.
(b) Is it possible to sketch a multigraph without loop and
with 1 connected component that has this degree sequence? If yes, sketch the multigraph.
If not, give a convincing argument why it is not possible.
(c) Is it possible to sketch a multigraph without loop and
with 2 connected components that has this degree sequence? If yes, sketch the multi-
graph. If not, give a convincing argument why it is not possible.
(d) Is it possible to sketch a multigraph without loop and
with 3 connected components that has this degree sequence? If yes, sketch the multi-
graph. If not, give a convincing argument why it is not possible.
(e) Is it possible to sketch a multigraph without loop and with
4 connected components that has this degree sequence? If yes, sketch the multigraph.
If not, give a convincing argument why it is not possible.
Consider the following degree sequence: {7, 7, 5, 5, 5, 3, 2, 2}.
(a) Is it possible to sketch a simple graph that has this degree
sequence? If yes, sketch the graph. If not, give a convincing argument why it is not
possible.
We recommend to first establish the number of vertices and edges of such a graph, if it
exists.
(b) Is it possible to sketch a multigraph without loop and
with 1 connected component that has this degree sequence? If yes, sketch the multigraph.
If not, give a convincing argument why it is not possible.
(c) Is it possible to sketch a multigraph without loop and
with 2 connected components that has this degree sequence? If yes, sketch the multi-
graph. If not, give a convincing argument why it is not possible.
(d) Is it possible to sketch a multigraph without loop and
with 3 connected components that has this degree sequence? If yes, sketch the multi-
graph. If not, give a convincing argument why it is not possible.
(e) Is it possible to sketch a multigraph without loop and with
4 connected components that has this degree sequence? If yes, sketch the multigraph.
If not, give a convincing argument why it is not possible.
