On the basis number of the corona of graphs

Mohammad Shakhatreh and Ahmad Al-Rhayyel

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-3

Abstract:

The basis number b ( G ) of a graph G is defined to be the leastinteger k such that G has a k -fold basis for its cyclespace. In this note, we determine the basis number of the coronaof graphs, in fact we prove that b ( v ∘ T ) = 2 for any tree andany 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 = G 1 ∘ G 2 is the corona of two graphs G 1 and G 2 , then b ( G 1 ) ≤ b ( G ) ≤ max ⁡ { b ( G 1 ) , b ( G 2 ) + 2 } , moreover we prove that if G is a Hamiltoniangraph, 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 thebasis number of the corona of some of special graphs.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:053712

DOI: 10.1155/IJMMS/2006/53712

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