Albertson energy and Albertson Estrada index of graphs


  • A. Jahanbani Department of Mathematics, Shahrood University of Technology, Shahrood, Iran

‎Let $G$ be a graph of order $n$ with vertices labeled as $v_1‎, ‎v_2,dots‎ , ‎v_n$‎. ‎Let $d_i$ be the degree of the vertex $v_i$ for $i = 1‎, ‎2‎, ‎cdots‎ , ‎n$‎. ‎The Albertson matrix of $G$ is the square matrix of order $n$ whose $(i‎, ‎j)$-entry is equal to $|d_i‎ - ‎d_j|$ if $v_i $ is adjacent to $v_j$ and zero‎, ‎otherwise‎. ‎The main purposes of this paper is to introduce the Albertson energy and Albertson-Estrada index of a graph‎, ‎both base on the eigenvalues of the Albertson matrix‎. ‎Moreover‎, ‎we establish upper and lower bounds for these new graph invariants and relations between them‎‎.

برای دانلود باید عضویت طلایی داشته باشید

برای دسترسی به متن کامل این مقاله و 10 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Towards the Albertson Conjecture

Albertson conjectured that if a graph G has chromatic number r, then the crossing number of G is at least as large as the crossing number of Kr, the complete graph on r vertices. Albertson, Cranston, and Fox verified the conjecture for r 6 12. In this paper we prove it for r 6 16. Dedicated to the memory of Michael O. Albertson.

متن کامل

The Estrada Index of Graphs

Let G be a simple n-vertex graph whose eigenvalues are λ1, . . . , λn. The Estrada index of G is defined as EE(G) = ∑n i=1 e λi . The importance of this topological index extends much further than just pure graph theory. For example, it has been used to quantify the degree of folding of proteins and to measure centrality of complex networks. The talk aims to give an introduction to the Estrada ...

متن کامل

Bounds of distance Estrada index of graphs

Let λ1, λ2, · · · , λn be the eigenvalues of the distance matrix of a connected graph G. The distance Estrada index of G is defined as DEE(G) = ∑ n i=1 ei . In this note, we present new lower and upper bounds for DEE(G). In addition, a Nordhaus-Gaddum type inequality for DEE(G) is given. MSC 2010: 05C12, 15A42.

متن کامل

Estrada Index of Random Bipartite Graphs

The topological structures of many social, biological, and technological systems can be characterized by the connectivity properties of the interaction pathways (edges) between system components (vertices) [1]. Starting with the Königsberg seven-bridge problem in 1736, graphs with bidirectional or symmetric edges have ideally epitomized structures of various complex systems, and have developed ...

متن کامل

Maximum Estrada index of bicyclic graphs

Let G be a simple graph of order n, let λ1(G), λ2(G), . . . , λn(G) be the eigenvalues of the adjacency matrix of G. The Esrada index of G is defined as EE(G) = ∑n i=1 e i. In this paper we determine the unique graph with maximum Estrada index among bicyclic graphs with fixed order.

متن کامل

The 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 کامل

ذخیره در منابع من

ذخیره در منابع من ذخیره شده در منابع من

{@ msg_add @}

  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی راحت تر خواهید کرد

دانلود متن کامل

برای دسترسی به متن کامل این مقاله و 10 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره 08  شماره 01

صفحات  11- 24

تاریخ انتشار 2019-02-01

با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.

میزبانی شده توسط پلتفرم ابری

copyright © 2015-2021