Bicyclic graphs with maximal revised Szeged index
نویسندگان
چکیده
e=uv∈E(nu(e)+n0(e)/2)(nv(e)+n0(e)/2), where nu(e) and nv(e) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u, and n0(e) is the number of vertices equidistant to u and v. Hansen used the AutoGraphiX and made the following conjecture about the revised Szeged index for a connected bicyclic graph G of order n ≥ 6:
منابع مشابه
On the revised edge-Szeged index of graphs
The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2) ), where mu(e|G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of ed...
متن کاملThe quotients between the (revised) Szeged index and Wiener index of graphs
Let Sz(G), Sz(G) and W (G) be the Szeged index, revised Szeged index and Wiener index of a graph G. In this paper, the graphs with the fourth, fifth, sixth and seventh largest Wiener indices among all unicyclic graphs of order n > 10 are characterized; and the graphs with the first, second, third, and fourth largest Wiener indices among all bicyclic graphs are identified. Based on these results...
متن کاملThe maximal total irregularity of some connected graphs
The total irregularity of a graph G is defined as 〖irr〗_t (G)=1/2 ∑_(u,v∈V(G))▒〖|d_u-d_v |〗, where d_u denotes the degree of a vertex u∈V(G). In this paper by using the Gini index, we obtain the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices.
متن کاملRevised Szeged Index of Product Graphs
The Szeged index of a graph G is defined as S z(G) = ∑ uv = e ∈ E(G) nu(e)nv(e), where nu(e) is number of vertices of G whose distance to the vertex u is less than the distance to the vertex v in G. Similarly, the revised Szeged index of G is defined as S z∗(G) = ∑ uv = e ∈ E(G) ( nu(e) + nG(e) 2 ) ( nv(e) + nG(e) 2 ) , where nG(e) is the number of equidistant vertices of e in G. In this paper,...
متن کاملPI, Szeged and Revised Szeged Indices of IPR Fullerenes
In this paper PI, Szeged and revised Szeged indices of an infinite family of IPR fullerenes with exactly 60+12n carbon atoms are computed. A GAP program is also presented that is useful for our calculations.
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 161 شماره
صفحات -
تاریخ انتشار 2013