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A connected graph with a unique cycle is called a unicyclic graph. A unicyclic graph with depth one may be thought of as being obtained from a cycle by appending ni pendent edges on each vertex vi in the cycle Ct (for some integer t⩾3), denoted by Cn1,n2,…,nt. In this paper, we give a complete characterization on the nullity of the line graph G=L(Cn1,n2,…,nt) as follows: Let m=#{i|ni>0}. Then(i)η(G)=2...
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