A CHARACTERIZATION OF (Cn;K1;n)-SUPERMAGIC OF TREES CORONA PATHS AND TREES JOIN A TRIVIAL GRAPH
Let H1 and H2 be two simple connected graphs. A graph G = (V (G);E(G)) admits an (H1;H2)-covering, where H1 and H2 are two subgraphs of G, if every edge in E(G) belongs to at least one subgraph of G isomorphic to H1 or H2. The graph G is called an (H1;H2)-magic, if there exists a bijective functi...
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| Format: | Theses |
| Language: | Indonesia |
| Subjects: | |
| Online Access: | https://digilib.itb.ac.id/gdl/view/32165 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let H1 and H2 be two simple connected graphs. A graph G = (V (G);E(G))
admits an (H1;H2)-covering, where H1 and H2 are two subgraphs of G, if every
edge in E(G) belongs to at least one subgraph of G isomorphic to H1 or H2. The
graph G is called an (H1;H2)-magic, if there exists a bijective function f : V (G) [
E(G) ! f1; 2; :::jV (G)j + jE(G)jg and two positive integers k1 and k2 such that
w(H
0
) =
X
v2V (H0 )
f(v) +
X
e2E(H0 )
f(e) = k1
for every subgraphs H0 of G isomorphic to H1 and
w(H
00
) =
X
v2V (H00 )
f(v) +
X
e2E(H00 )
f(e) = k2:
for every subgraphs H0 of G isomorphic to H1. Furthermore, G is called (H1;H2)-
supermagic, if f(V (G)) ! f1; 2; :::; jV (G)jg.
A graph G corona graph H, denoted by GH is a graph which is obtained from G
and jV (G)j copies of H, namely H1;H2; :::;HjV (G)j, and joined every vi 2 V (G)
to all vertices in V (Hi) for i 2 f1; 2; :::; jV (G)jg. In this thesis, we give a necessary
condition of G being a (Cn;K1;n)-magic, and a characterization of (Cn;K1;n)-
supermagic of trees corona paths T Pm for any n 3 and m 2. Besides that,
we study a characterization of (Cn;K1;n)-supermagic of trees join a trivial graph
T + K1 for n 2 f3; 4g. The graph G join H denoted by G + H is a graph that is
obtained from G union H and joined every vertex in G to all vertices in H. |
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