On the basis number of the corona of graphs
نویسندگان
چکیده
The basis number b(G) of a graphG is defined to be the least integer k such thatG has a kfold 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 inT , 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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عنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2006 شماره
صفحات -
تاریخ انتشار 2006