منابع مشابه
A Note on the Nullity of Unicyclic Graphs
The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. In this paper we show the expression of the nullity and nullity set of unicyclic graphs with n vertices and girth r, and characterize the unicyclic graphs with extremal nullity.
متن کاملOn the nullity of graphs
The nullity of a graph G, denoted by η(G), is the multiplicity of the eigenvalue zero in its spectrum. It is known that η(G) ≤ n − 2 if G is a simple graph on n vertices and G is not isomorphic to nK1. In this paper, we characterize the extremal graphs attaining the upper bound n− 2 and the second upper bound n− 3. The maximum nullity of simple graphs with n vertices and e edges, M(n, e), is al...
متن کاملA short note on the nullity theorem
In this paper we take a close look at the nullity theorem as formulated by Markham and Fiedler in 1986. The theorem is a valuable tool in the computations with structured rank matrices, it connects ranks of subblocks of an invertible matrix A with ranks of other subblocks in his inverse A. A little earlier, Barrett and Feinsilver, 1981, proved a theorem very close to the nullity theorem, but re...
متن کاملOn the Eccentric Connectivity Index of Unicyclic Graphs
In this paper, we obtain the upper and lower bounds on the eccen- tricity connectivity index of unicyclic graphs with perfect matchings. Also we give some lower bounds on the eccentric connectivity index of unicyclic graphs with given matching numbers.
متن کاملOn reverse degree distance of unicyclic graphs
The reverse degree distance of a connected graph $G$ is defined in discrete mathematical chemistry as [ r (G)=2(n-1)md-sum_{uin V(G)}d_G(u)D_G(u), ] where $n$, $m$ and $d$ are the number of vertices, the number of edges and the diameter of $G$, respectively, $d_G(u)$ is the degree of vertex $u$, $D_G(u)$ is the sum of distance between vertex $u$ and all other vertices of $G$, and $V(G)$ is the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics
سال: 2014
ISSN: 2152-7385,2152-7393
DOI: 10.4236/am.2014.510156