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On the nullity of the line graph of unicyclic graph with depth one
- Source :
-
Linear Algebra & its Applications . Oct2012, Vol. 437 Issue 8, p2038-2055. 18p. - Publication Year :
- 2012
-
Abstract
- Abstract: 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 pendent edges on each vertex in the cycle (for some integer ), denoted by . In this paper, we give a complete characterization on the nullity of the line graph as follows: Let . Then [(i)] if and only if and . [(ii)] if and only if and either [(1)] for , the length of any zero chain of is even and ; or [(2)] and one of and must hold. [(iii)] , otherwise. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 437
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 78145752
- Full Text :
- https://doi.org/10.1016/j.laa.2012.05.028