Extremal Stable Graphs
نویسندگان
چکیده
منابع مشابه
Eccentric Connectivity Index: Extremal Graphs and Values
Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine ...
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 کاملThe Extremal Graphs for (Sum-) Balaban Index of Spiro and Polyphenyl Hexagonal Chains
As highly discriminant distance-based topological indices, the Balaban index and the sum-Balaban index of a graph $G$ are defined as $J(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)D_{G}(v)}}$ and $SJ(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)+D_{G}(v)}}$, respectively, where $D_{G}(u)=sumlimits_{vin V}d(u,v)$ is the distance sum of vertex $u$ in $G$, $m$ is the n...
متن کاملOn (Kq;k)-Stable Graphs
A graph G is called (H; k)-vertex stable if G contains a subgraph isomorphic to H even after removing any k of its vertices. By stab(H; k) we denote the minimum size among the sizes of all (H; k)-vertex stable graphs. Given an integer q ≥ 2, we prove that, apart of some small values of k, stab(Kq; k) = (2q−3)(k+1). This confirms in the affirmative the conjecture of Dudek et al. [(H, k) stable g...
متن کاملA Novel Image Structural Similarity Index Considering Image Content Detectability Using Maximally Stable Extremal Region Descriptor
The image content detectability and image structure preservation are closely related concepts with undeniable role in image quality assessment. However, the most attention of image quality studies has been paid to image structure evaluation, few of them focused on image content detectability. Examining the image structure was firstly introduced and assessed in Structural SIMilarity (SSIM) measu...
متن کاملFibonacci Index and Stability Number of Graphs: a Polyhedral Study
The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Turán graphs frequently appear in extremal graph theory. We show that Turán graphs and a conne...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009