The Wiener Index of Unicyclic Graphs with Girth and Matching Number

نویسندگان

  • Ya-Hong Chen
  • Xiao-Dong Zhang
چکیده

In this paper, we investigate how the Wiener index of unicyclic graphs varies with graph operations. These results are used to present a sharp lower bound for the Wiener index of unicyclic graphs of order n with girth and the matching number β ≥ 3g 2 . Moreover, we characterize all extremal graphs which attain the lower bound.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The hyper-Wiener index of unicyclic graphs with given matching number

We determine the minimum hyper-Wiener index of unicyclic graphs with given number of vertices and matching number, and characterize the extremal graphs. Mathematics Subject Classification (2010): 05C12, 05C35, 05C90.

متن کامل

On the Wiener Index of Unicyclic Graphs

The Wiener index of a graph G is defined as W (G) = ∑ u,v dG(u, v), where dG(u, v) is the distance between u and v in G, and the sum goes over all pairs of vertices. In this paper, we characterize the connected unicyclic graph with minimum Wiener indices among all connected unicyclic graphs of order n and girth g with k pendent vertices.

متن کامل

On 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 کامل

The second geometric-arithmetic index for trees and unicyclic graphs

Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree o...

متن کامل

Minimum Wiener Indices of Trees and Unicyclic Graphs of given Matching Number

The Wiener index of a connected graph is defined as the sum of distances between all unordered pairs of its vertices. We determine the minimum Wiener indices of trees and unicyclic graphs with given number of vertices and matching number, respectively. The extremal graphs are characterized.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Ars Comb.

دوره 106  شماره 

صفحات  -

تاریخ انتشار 2012