the emph{harary index} $h(g)$ of a connected graph $g$ is defined as $h(g)=sum_{u,vin v(g)}frac{1}{d_g(u,v)}$ where $d_g(u,v)$ is the distance between vertices $u$ and $v$ of $g$. the steiner distance in a graph, introduced by chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. for a connected graph $g$ of order at least $2$ and $ssubseteq v(g)$, th...

Let G be a graph with vertex and edge sets V(G) and E(G), respectively. As usual, the distance between the vertices u and v of a connected graph G is denoted by d(u,v) and it is defined as the number of edges in a minimal path connecting the vertices u and v. Throughout the paper, a graph means undirected connected graph without loops and multiple edges. In chemical graph theory, a molecular gr...

abstract. topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. graph theory is a delightful playground for the exploration of proof techniques in discrete mathematics and its results have applications in many areas of sciences. a graph is a ...

Abstract This work explores the following applications of graph theory to plasma chemical reaction engineering: assembly a weighted directional with key addition nodes, from published set data for air; visualisation probing network potentially useful or problematic pathways; running Dijkstra’s algorithm between all species nodes; further analysis engineering information such as which conditions...

An outerplanar graph is a planar graph which can be embedded in the plane in such a way that all of vertices lie on the outer boundary. Many chemical compounds are known to be expressed by outerplanar graphs. An externally extensible outerplanar graph pattern (eeo-graph pattern for short) represents a graph pattern common to a finite set of outerplanar graphs like a dataset of chemical compound...

Graph-theoretical methods have revolutionized the exploration of complex systems across scientific disciplines. Here, we demonstrate their applicability to investigation and comparison three widely used atmospheric chemical mechanisms varying complexity: Master Chemical Mechanism v3.3, GEOS-Chem v12.6, Super-Fast mechanism. We investigate these using a class graphical models known as species-re...

Molecular representation learning contributes to multiple downstream tasks such as molecular property prediction and drug design. To properly represent molecules, graph contrastive is a promising paradigm it utilizes self-supervision signals has no requirements for human annotations. However, prior works fail incorporate fundamental domain knowledge into semantics thus ignore the correlations b...

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph $G$ denoted by $chi_a '(G)$ is the minimum number $k$ such that there is an acyclic edge coloring using $k$ colors. The maximum degree in $G$ denoted by $Delta(G)$, is the lower bound for $chi_a '(G)$. $P$-cuts introduced in this paper acts as a powerfu...