Geometric group theory and arithmetic diameter
نویسندگان
چکیده
منابع مشابه
Trees with Given Diameter and Minimum Second Geometric–Arithmetic Index∗
The second geometric-arithmetic index GA2(G) of a graph G was introduced recently by Fath-Tabar et al. [2] and is defined to be ∑ uv∈E(G) √ nu(e,G)nv(e,G) 1 2 [nu(e,G)+nv(e,G)] , where e = uv is one edge in G, and nu(e,G) denotes the number of vertices in G lying closer to u than to v. In this paper, we characterize the tree with the minimum GA2 index among the set of trees with given order and...
متن کاملGeometric Group Theory Notes
Definition. Let Γ be a group. Take A ⊂ Γ to be any subset. The subgroup generated by A, denoted 〈A〉, is the smallest subgroup of Γ containing A. Equivalently, 〈A〉 is the intersection of all subgroups of Γ containing A. Equivalently, 〈A〉 = {a1 1 · · · an n | ai ∈ A, ǫi = ±1}, the set of finite products of elements of A ∪A−1. Notation. We will frequently use Γ to denote a group. If A is a set, A ...
متن کاملThe 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 کاملOn Second Geometric-Arithmetic Index of Graphs
The concept of geometric-arithmetic indices (GA) was put forward in chemical graph theory very recently. In spite of this, several works have already appeared dealing with these indices. In this paper we present lower and upper bounds on the second geometric-arithmetic index (GA2) and characterize the extremal graphs. Moreover, we establish Nordhaus-Gaddum-type results for GA2.
متن کاملOn Third Geometric-Arithmetic Index of Graphs
Continuing the work K. C. Das, I. Gutman, B. Furtula, On second geometric-arithmetic index of graphs, Iran. J. Math Chem., 1(2) (2010) 17-28, in this paper we present lower and upper bounds on the third geometric-arithmetic index GA3 and characterize the extremal graphs. Moreover, we give Nordhaus-Gaddum-type result for GA3.
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ژورنال
عنوان ژورنال: Publicationes Mathematicae Debrecen
سال: 2011
ISSN: 0033-3883
DOI: 10.5486/pmd.2011.5087