The inertia of weighted unicyclic graphs
نویسندگان
چکیده
منابع مشابه
The Inertia of Unicyclic Graphs and Bicyclic Graphs
Let G be a graph with n vertices and ν(G) be the matching number of G. The inertia of a graph G, In(G) = (n+, n−, n0) is an integer triple specifying the numbers of positive, negative and zero eigenvalues of the adjacency matrix A(G), respectively. Let η(G) = n0 denote the nullity of G (the multiplicity of the eigenvalue zero of G). It is well known that if G is a tree, then η(G) = n− 2ν(G). Gu...
متن کاملThe extremal problems on the inertia of weighted bicyclic graphs
LetGw be a weighted graph. The number of the positive, negative and zero eigenvalues in the spectrum of Gw are called positive inertia index, negative inertia index and nullity of Gw, and denoted by i+(Gw), i−(Gw), i0(Gw), respectively. In this paper, sharp lower bound on the positive (resp. negative) inertia index of weighted bicyclic graphs of order n with pendant vertices is obtained. Moreov...
متن کاملOn the inertia of weighted (k−1)-cyclic graphs∗
Let Gw be a weighted graph. The inertia of Gw is the triple In(Gw) = (i+(Gw), i−(Gw), i0(Gw)), where i+(Gw), i−(Gw), i0(Gw) are, respectively, the number of the positive, negative and zero eigenvalues of the adjacency matrix A(Gw) of Gw including their multiplicities. A simple n-vertex connected graph is called a (k − 1)-cyclic graph if its number of edges equals n + k − 2. Let θ(r1, r2, . . . ...
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 کاملThe Signless Laplacian Estrada Index of Unicyclic Graphs
For a simple graph $G$, the signless Laplacian Estrada index is defined as $SLEE(G)=sum^{n}_{i=1}e^{q^{}_i}$, where $q^{}_1, q^{}_2, dots, q^{}_n$ are the eigenvalues of the signless Laplacian matrix of $G$. In this paper, we first characterize the unicyclic graphs with the first two largest and smallest $SLEE$'s and then determine the unique unicyclic graph with maximum $SLEE$ a...
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: Linear Algebra and its Applications
سال: 2014
ISSN: 0024-3795
DOI: 10.1016/j.laa.2014.01.023