BSc Mathematics SEM V 2016 17 2016-17 Elective Graph Theory Question Paper - Mumbai University | munotes
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2016-17 - Graph Theory & Combinatorics
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Questions asked in this paper
- Figures to the right indcate full marks
Q.P. Code :
Figures to the right indcate full marks
“Show thet a nontrivial graph is bipartite if and only if it contains cycle
self complementary graph. If G is self complementar f ord
connected and p = 0 or 1(. mod 4) st
adjacency matrix of a graph G. If G is a vertex set V(G) =
and adjacency matrix A = that the entry at) in
i column of A* is the number of — walks of length k in G
G and H ere isomorphic graphs , then show degree sequence of the vertices
of G are the same as the degree sequence of of H
EE graph of size g, then degu = Hence prove that every
has an even number of odd
Dijkstra’s Algorithm to find test path in a graph G
Attempt any ONE question: (8)
“i, State and prove Cayley’s formu for spanning trees
Define a cut vertex of a graph Show that every nontrivial graph contains at least
vertices which are vertices
any TWO questions 7 (12)
Define spanning tree a graph G. Show that a graph is connected if and only if it
ii, Show. a (p, graph G, p 2 3, contains a cut edge, then it: must
& Is the converse true?
Show that there exist a tree with degree sequence > dg d, if and only
d write Depth First Search Algorithm for finding spanning tree
auch that deg (u) + deg(v) =
(a) Attempt p prove that G is
on ond terian if and only if ever,
non t is Vert \
any Show that and
; ii, Show that graph 2
js Hamiltonian if and only if-its
that y edges with ROS. I
G be a simple graph with
graph on p. vertices and > then that G is @ connecteg
denotes the minim imum degree
State Havel-Haldmi Theorem for of G. Using this th
(c) Describ algo rithm for anning tree in a con;
Show thats vertex v in tree if
(e) Show. that there are n deg (v) >
3:5, ere are edge dis 1
disjoint: Hamiltonian in in Als
Figures to the right indcate full marks
“Show thet a nontrivial graph is bipartite if and only if it contains cycle
self complementary graph. If G is self complementar f ord
connected and p = 0 or 1(. mod 4) st
adjacency matrix of a graph G. If G is a vertex set V(G) =
and adjacency matrix A = that the entry at) in
i column of A* is the number of — walks of length k in G
G and H ere isomorphic graphs , then show degree sequence of the vertices
of G are the same as the degree sequence of of H
EE graph of size g, then degu = Hence prove that every
has an even number of odd
Dijkstra’s Algorithm to find test path in a graph G
Attempt any ONE question: (8)
“i, State and prove Cayley’s formu for spanning trees
Define a cut vertex of a graph Show that every nontrivial graph contains at least
vertices which are vertices
any TWO questions 7 (12)
Define spanning tree a graph G. Show that a graph is connected if and only if it
ii, Show. a (p, graph G, p 2 3, contains a cut edge, then it: must
& Is the converse true?
Show that there exist a tree with degree sequence > dg d, if and only
d write Depth First Search Algorithm for finding spanning tree
auch that deg (u) + deg(v) =
(a) Attempt p prove that G is
on ond terian if and only if ever,
non t is Vert \
any Show that and
; ii, Show that graph 2
js Hamiltonian if and only if-its
that y edges with ROS. I
G be a simple graph with
graph on p. vertices and > then that G is @ connecteg
denotes the minim imum degree
State Havel-Haldmi Theorem for of G. Using this th
(c) Describ algo rithm for anning tree in a con;
Show thats vertex v in tree if
(e) Show. that there are n deg (v) >
3:5, ere are edge dis 1
disjoint: Hamiltonian in in Als
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