Related papers: Maximum augmented Zagreb index on polyomino chains

For a simple graph $G$ with $n$ vertices and $m$ edges, the first Zagreb index and the second Zagreb index are defined as $M_1(G)=\sum_{v\in V}d(v)^2 $ and $M_2(G)=\sum_{uv\in E}d(u)d(v)$. In \cite{VGFAD}, it was shown that if a connected…

The degree sequence optimization problem is to find a subgraph of a given graph which maximizes the sum of given functions evaluated at the subgraph degrees. Here we study this problem by replacing degree sequences, via suitable nonlinear…

This paper leverages the framework of algorithms-with-predictions to design data structures for two fundamental dynamic graph problems: incremental topological ordering and cycle detection. In these problems, the input is a directed graph…

We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…

In this paper we show a new way of constructing deterministic polynomial-time approximation algorithms for computing complex-valued evaluations of a large class of graph polynomials on bounded degree graphs. In particular, our approach…

The problem of efficiently sampling from a set of(undirected) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the sampling. The…

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…

We show that there exist linear-time algorithms that compute the strong chromatic index of Halin graphs, of maximal outerplanar graphs and of distance-hereditary graphs.

EPG graphs, introduced by Golumbic et al. in 2009, are edge-intersection graphs of paths on an orthogonal grid. The class $B_k$-EPG is the subclass of EPG graphs where the path on the grid associated to each vertex has at most $k$ bends.…

A polyomino is a polygonal region with axis parallel edges and corners of integral coordinates, which may have holes. In this paper, we consider planar tiling and packing problems with polyomino pieces and a polyomino container $P$. We give…

Let $\mathcal{C}_{n,k}$ be the family of all cacti with $k$ cycles and $n\geq4$ vertices. In the present note, the element of the class $\mathcal{C}_{n,k}$ having minimum augmented Zagreb index ($AZI$) is characterized. Moreover, some…

The complementary second Zagreb index of a graph $G$ is defined as $cM_2(G)=\sum_{uv\in E(G)}|(d_u(G))^2-(d_v(G))^2|$, where $d_u(G)$ denotes the degree of a vertex $u$ in $G$ and $E(G)$ represents the edge set of $G$. Let $G^*$ be a graph…

Finding an efficient optimal partial tiling algorithm is still an open problem. We have worked on a special case, the tiling of Manhattan polyominoes with dominoes, for which we give an algorithm linear in the number of columns. Some…

We investigate several related measures of peripherality and centrality for vertices and edges in networks, including the Mostar index which was recently introduced as a measure of peripherality for both edges and networks. We refute a…

In this paper, we develop two zonotope-based set-membership estimation algorithms for identification of time-varying parameters in linear models, where both additive and multiplicative uncertainties are treated explicitly. The two recursive…

We develop terminology and methods for working with maximally oriented partially directed acyclic graphs (maximal PDAGs). Maximal PDAGs arise from imposing restrictions on a Markov equivalence class of directed acyclic graphs, or…

This article provides structural characterization of simple graphs whose edge-set can be partitioned into maximum matchings. We use Vizing's classification of simple graphs based on edge chromatic index.

Let $G=(V, E)$ be a graph where $V(G)$ and $E(G)$ are the vertex and edge sets, respectively. In a graph $G$, two edges $e_1, e_2\in E(G)$ are said to have a \emph{common edge} $e\neq e_1, e_2$ if $e$ joins an endpoint of $e_1$ to an…

Let $G$ be a connected graph. The resistance distance between any two vertices of $G$ is equal to the effective resistance between them in the corresponding electrical network constructed from $G$ by replacing each edge with a unit…

Modern materials science has historically been founded on combining restricted subsets of the periodic table, favoring high-purity, few-element systems. However, the demands of an emerging circular economy, together with the need to…