Related papers: Note on VDB Topological Indices of k-Cyclic Graphs

Let $G=(V(G),E(G))$ be a graph and $d(v)$ be the degree of the vertex $v\in V(G)$. The exponential reduced Sombor index of $G$, denoted by $e^{SO_{red}}(G)$, is defined as $$e^{SO_{red}}(G)=\sum_{uv\in…

In theoretical chemistry molecular structure descriptors are used for modeling physico-chemical, pharmacological, toxicologic, biological and other properties of chemical compounds. In this paper we study distance-based graph invariants and…

In the Survivable Network Design Problem (SNDP), the input is an edge-weighted (di)graph $G$ and an integer $r_{uv}$ for every pair of vertices $u,v\in V(G)$. The objective is to construct a subgraph $H$ of minimum weight which contains…

Let $G$ be a graph. Denote by $d_x$, $E(G)$, and $D(G)$ the degree of a vertex $x$ in $G$, the set of edges of $G$, and the degree set of $G$, respectively. This paper proposes to investigate (both from mathematical and applications points…

Elliptic Sombor and Euler Sombor indices are recently defined topological indices using Sombor index. Elliptic sombor index is defined as $ESO(G)=\sum_{uv\in E(G)}(d_u+ d_v)\sqrt{d^2_u+ d^2_v}$ and Euler Sombor index is defined as $EU(G)=…

A graph $G$ is $k$-path-coverable if its vertex set $V(G)$ can be covered by $k$ or fewer vertex disjoint paths. In this paper, using the $Q$-index of a connected graph $G$, we present a tight sufficient condition for $G$ with fixed minimum…

Let $G=(V,E)$ be a simple connected graph with vertex set $V(G)$ and edge set $E(G)$. The third atom-bond connectivity index, $ABC_3$ index, of $G$ is defined as $ABC_3(G)=\sum\limits_{uv\in E(G)}\sqrt{\frac{e(u)+e(v)-2}{e(u)e(v)}}$, where…

Let $G$ be a graph and $f:V(G)\rightarrow \mathbb{N}$ be a function. An $f$-coloring of a graph $G$ is an edge coloring such that each color appears at each vertex $v\in V(G)$ at most $f (v)$ times. The minimum number of colors needed to…

Let $I(G)$ be a topological index of a graph. If $I(G+e)<I(G)$ (or $I(G+e)>I(G)$, respectively) for each edge $e\not\in G$, then $I(G)$ is monotonically decreasing (or increasing, respectively) with the addition of edges. In this article,…

Let $G$ be a simple undirected graph with vertex set $V(G)=\{v_1, v_2, \ldots, v_n\}$ and edge set $E(G)$. The Sombor matrix $\mathcal{S}(G)$ of a graph $G$ is defined so that its $(i,j)$-entry is equal to $\sqrt{d_i^2+d_j^2}$ if the…

For a graph $G$ and a positive integer $k$, a vertex labelling $f:V(G)\to\{1,2\ldots,k\}$ is said to be $k$-distinguishing if no non-trivial automorphism of $G$ preserves the sets $f^{-1}(i)$ for each $i\in\{1,\ldots,k\}$. The…

Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds…

Given an edge labeling $f$ of a graph $G$, a vertex $v$ is called an $AR$-vertex, if $v$ has distinct edge weight sums for each distinct subset of edges incident on $v$. An injective edge labeling $f$ of a graph $G$ is called an…

A total coloring of a simple undirected graph $G$ is an assignment of colors to its vertices and edges such that the colors given to the vertices form a proper vertex coloring, the colors given to the edges form a proper edge coloring, and…

The atom-bond connectivity (ABC) index is a degree-based molecular structure descriptor that can be used for modelling thermodynamic properties of organic chemical compounds. Motivated by its applicable potential, a series of investigations…

The Wiener index of a connected graph is defined as the sum of the distances between all unordered pair of its vertices. In this paper, we characterize the graphs which extremize the Wiener index among all graphs on $n$ vertices with $k$…

The Wiener index of a strong digraph $D$ is defined as the sum of the distances between all ordered pairs of vertices. This definition has been extended to digraphs that are not necessarily strong by defining the distance from a vertex $a$…

A topological index of a graph $G$ is a numerical quantity that describes its topology. Reverse degree-based topological indices play an important role in finding topological descriptors. Azacitidine, Decitabine, and Guadecitabine are…

If V is the vertex sequence of a symmetric 2t-cycle in the hypercube graph with the vertices {1,-1}^t, then for any vertex T of the graph there exists a unique inclusion-minimal subset of V such that T is the sum of its elements. We present…

Given a simple connected non-directed graph $G=(V(G),E(G))$, we consider two families of graph invariants: $RX_\Sigma(G) = \sum_{uv \in E(G)} F(r_u,r_v)$ (which has gained interest recently) and $RX_\Pi(G) = \prod_{uv \in E(G)} F(r_u,r_v)$…