Related papers: Eccentric Connectivity Index of Chemical Trees
We investigate the structure of trees that have minimal algebraic connectivity among all trees with a given degree sequence. We show that such trees are caterpillars and that the vertex degrees are non-decreasing on every path on…
The subtrees and BC-subtrees (subtrees where any two leaves are at even distance apart) have been extensively studied in recent years. Such structures, under special constraints on degrees, have applications in many fields. Through an…
The total reciprocal edge-eccentricity is a novel graph invariant with vast potential in structure activity/property relationships. This graph invariant displays high discriminating power with respect to both biological activity and…
The energy of a molecular graph is a popular parameter that is defined as the sum of the absolute values of a graph's eigenvalues. It is well known that the energy is related to the matching polynomial and thus also to the Hosoya index via…
We propose a new method to estimate a root-directed spanning tree from extreme data. A prominent example is a river network, to be discovered from extreme flow measured at a set of stations. Our new algorithm utilizes qualitative aspects of…
Vertex-degree-based topological indices have recently gained a lot of attention from mathematical chemists. One such index that we focus on in this paper is called Sombor index. After its definition in late 2020, the Sombor index was…
Let $\mathbb{G} = (\mathcal{V}, \mathcal{E})$ be a simple connected graph, where $\mathcal{V}$ and $\mathcal{E}$ denote the vertex and edge sets, respectively. The first Zagreb index is defined as $\mathcal{M}_{1}(\mathbb{G}) = \sum_{v \in…
In a study on the structure--dependency of the total $\pi$-electron energy from 1972, Trinajsti\'c and one of the present authors have shown that it depends on the sums $\sum_{v\in V}d(v)^2$ and $\sum_{v\in V}d(v)^3$, where $d(v)$ is the…
The information rate for an access structure is the reciprocal of the load of the optimal secret sharing scheme for this structure. We determine this value for all trees: it is 1/(2-1/c), where c is the size of the largest core of the tree.…
We propose a family of graph structural indices related to the Matrix-forest theorem. The properties of the basic index that expresses the mutual connectivity of two vertices are studied in detail. The derivative indices that measure…
The Steiner distance of vertices in a set $S$ is the minimum size of a connected subgraph that contain these vertices. The sum of the Steiner distances over all sets $S$ of cardinality $k$ is called the Steiner $k$-Wiener index and studied…
In this paper, we investigate the structures of an extremal tree which has the minimal number of subtrees in the set of all trees with the given degree sequence of a tree. In particular, the extremal trees must be caterpillar and but in…
We study the Steiner $k$-eccentricity on trees, which generalizes the previous one in the paper [X.~Li, G.~Yu, S.~Klav\v{z}ar, On the average Steiner 3-eccentricity of trees, arXiv:2005.10319, 2020]. To support the algorithm, we achieve…
There are various topological indices such as degree based topological indices, distance based topological indices and counting related topological indices etc. These topological indices correlate certain physicochemical properties such as…
The arithmetic-geometric index is a newly proposed degree-based graph invariant in mathematical chemistry. We give a sharp upper bound on the value of this invariant for connected chemical graphs of given order and size and characterize the…
We investigate the structure of trees that have greatest maximum eigenvalue among all trees with a given degree sequence. We show that in such an extremal tree the degree sequence is non-increasing with respect to an ordering of the…
We study the stochastic dynamics of strongly-coupled excitable elements on a tree network. The peripheral nodes receive independent random inputs which may induce large spiking events propagating through the branches of the tree and leading…
Although the analysis of rooted tree shape has wide-ranging applications, notions of tree balance have developed independently in different domains. In computer science, a balanced tree is one that enables efficient updating and retrieval…
The eccentricity matrix $\varepsilon(G)$ of a graph $G$ is constructed from the distance matrix of $G$ by keeping only the largest distances for each row and each column. This matrix can be interpreted as the opposite of the adjacency…
We present an explicit connected spanning structure that appears in a random graph just above the connectivity threshold with high probability.