• A simple graph is called regular if every vertex of the graph has the same degree. An N-regular graph is a graph with every vertex with degree n. • The graph of cycle denoted by C, for n > 3, consists of n vertices v1, v2, ..., Un and edges {v1, v2}, {2, 03}, ..-. {On-1; on} and {vn. v1}. • The graph of wheel denoted by Wn is obtained when an additional vertex is added to cycle Cn, for n > 3. and connect this new vertex to each of n vertices by new edges.. 3.(a) Draw C6, C7. W6 and W,. 3.(b) Are C, and W, regular graphs? Justify your answer. 3.(c) How many edges and vertices do C6, C7, W6 and W, have? be the number of edges of W, and b, be the number of edges of Cn, Find a recurrence relation for ɑ1, a2, a3, . . . and b1, b2, b3, ... . Guess the explicit formula for an and b,. Justify 3. (d) Let An your ansWer. 3.(e) For which values of n do Wn and C, have Euler circuit? Justify your answer. 3. (f) For which values of n does W have Hamiltonian circuit? If so, label the vertices and find O REDMINOTEgPRO circuit. AI QUAD CAMERA 3.(g) For which values of n do Wn and C, are bipartite? Justify your answer.

• A simple graph is called regular if every vertex of the graph has the same degree. An N-regular graph is a graph with every vertex with degree n. • The graph of cycle denoted by C, for n > 3, consists of n vertices v1, v2, ..., Un and edges {v1, v2}, {2, 03}, ..-. {On-1; on} and {vn. v1}. • The graph of wheel denoted by Wn is obtained when an additional vertex is added to cycle Cn, for n > 3. and connect this new vertex to each of n vertices by new edges.. 3.(a) Draw C6, C7. W6 and W,. 3.(b) Are C, and W, regular graphs? Justify your answer. 3.(c) How many edges and vertices do C6, C7, W6 and W, have? be the number of edges of W, and b, be the number of edges of Cn, Find a recurrence relation for ɑ1, a2, a3, . . . and b1, b2, b3, ... . Guess the explicit formula for an and b,. Justify 3. (d) Let An your ansWer. 3.(e) For which values of n do Wn and C, have Euler circuit? Justify your answer. 3. (f) For which values of n does W have Hamiltonian circuit? If so, label the vertices and find O REDMINOTEgPRO circuit. AI QUAD CAMERA 3.(g) For which values of n do Wn and C, are bipartite? Justify your answer.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

• A simple graph is called regular if every vertex of the graph has the same degree. An
n-regular graph is a graph with every vertex with degree n.
• The graph of cycle denoted by C, for n > 3, consists of n vertices v1, v2, ..., Un and
edges {v1, v2}, {2, 03}, ..-- {On-1; on} and {vn. v1}.
• The graph of wheel denoted by W is obtained when an additional vertex is added to
cycle Cn, for n > 3. and connect this new vertex to each of n vertices by new edges.
3.(a) Draw C6, C7. W6 and W-.
3.(b) Are C, and W, regular graphs? Justify your answer.
3.(c) How many edges and vertices do C6, C7, W6 and W, have?
3. (d) Let
relation for a1, a2, a3, . . . and b1, b2, 63, . ..
be the number of edges of W, and b, be the number of edges of Cn, Find a recurrence
Guess the explicit formula for an and b. Justify
An
your answWer.
3.(e) For which values of n do Wn and C, have Euler circuit? Justify your answer.
3. (f) For which values of n does W have Hamiltonian circuit? If so, label the vertices and find
DO REDMI NOiCgnRRO circuit.
AI QUAD CAMERA
3.(g) For which values of n do W, and C, are bipartite? Justify your answer.

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