On the basis number of the corona of graphs
The basis number b(G) of a graph G is defined to be the least integer k such that G has a k-fold basis for its cycle space. In this note, we determine the basis number of the corona of graphs, in fact we prove that b(v∘T)=2 for any tree and any vertex v not in T, b(v∘H)≤b(H)+2, where H is any graph...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/53712 |
| Summary: | The basis number b(G) of a graph G is defined to be the least
integer k such that G has a k-fold basis for its cycle
space. In this note, we determine the basis number of the corona
of graphs, in fact we prove that b(v∘T)=2 for any tree and
any vertex v not in T, b(v∘H)≤b(H)+2, where H is any graph and v is not a vertex of H, also we prove that if
G=G1∘G2 is the corona of two graphs G1 and
G2, then b(G1)≤b(G)≤max{b(G1),b(G2)+2}, moreover we prove that if G is a Hamiltonian
graph, then b(v∘G)≤b(G)+1, where v is any vertex not in G, and finally we give a sequence of remarks which gives the
basis number of the corona of some of special graphs. |
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| ISSN: | 0161-1712 1687-0425 |