相关论文: Maximum augmented Zagreb index on polyomino chains
It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…
In this paper, we exhibit an irreducible Markov chain $M$ on the edge $k$-colorings of bipartite graphs based on certain properties of the solution space. We show that diameter of this Markov chain grows linearly with the number of edges in…
Molecule optimization is an important problem in chemical discovery and has been approached using many techniques, including generative modeling, reinforcement learning, genetic algorithms, and much more. Recent work has also applied…
In the original article ``Wiener index of Eulerian graphs'' [Discrete Applied Mathematics Volume 162, 10 January 2014, Pages 247-250], the authors state that the Wiener index (total distance) of an Eulerian graph is maximized by the cycle.…
In this paper, we prove a collection of results on graphical indices. We determine the extremal graphs attaining the maximal generalized Wiener index (e.g. the hyper-Wiener index) among all graphs with given matching number or independence…
The problem of finding a maximum $2$-matching without short cycles has received significant attention due to its relevance to the Hamilton cycle problem. This problem is generalized to finding a maximum $t$-matching which excludes specified…
The Maximum Induced Matching problem asks to find the maximum $k$ such that, given a graph $G=(V,E)$, can we find a subset of vertices $S$ of size $k$ for which every vertices $v$ in the induced graph $G[S]$ has exactly degree $1$. In this…
In this paper we present a theoretical analysis in order to establish maximal and minimal vectors with respect to the majorization order of particular subsets of \Re ^n: Afterwards we apply these issues to the calcula- tion of bounds for a…
The Longest Path Problem is a question of finding the maximum length between pairs of vertices of a graph. In the general case, the problem is NP-complete. However, there is a small collection of graph classes for which there exists an…
Let G be a graph with vertex set V (G) and edge set E(G). The first generalized multiplicative Zagreb index of G is M_1(G) and the second multiplicative Zagreb index is M_2(G). The multiplicative Zagreb indices have been the focus of…
We consider hypergraph network design problems where the goal is to construct a hypergraph that satisfies certain connectivity requirements. For graph network design problems where the goal is to construct a graph that satisfies certain…
The Kirchhoff index of a connected graph is the sum of resistance distances between all unordered pairs of vertices in the graph. Its considerable applications are found in a variety of fields. In this paper, we determine the maximum value…
Protein structural alignment is an important problem in computational biology. In this paper, we present first successes on provably optimal pairwise alignment of protein inter-residue distance matrices, using the popular Dali scoring…
In this paper, we solve a maximization problem where the objective function is quadratic and the constraints set is the reachable values set of a stable discrete-time affine system. This problem is equivalent to solve an infinite number of…
Xu in 2011 determined the largest value of the second Zagreb index in an $n$-vertex graph $G$ with clique number $k$, and also the smallest value with the additional assumption that $G$ is connected. We extend these results to other…
The aim of this paper is to obtain new inequalities for a large family of topological indices restricted to unicyclic graphs and to characterize the set of extremal unicyclic graphs with respect to them. This family includes variable first…
For a given graph $G$, a maximum internal spanning tree of $G$ is a spanning tree of $G$ with maximum number of internal vertices. The Maximum Internal Spanning Tree (MIST) problem is to find a maximum internal spanning tree of the given…
Mathematical crystal chemistry views crystal structures as the optimal solutions of mathematical optimization problem formalizing inorganic structural chemistry. This paper introduces the minimum and maximum atomic radii depending on the…
The Kirchhoff index is defined as the sum of resistance distances between all pairs of vertices in a graph. This index is a critical parameter for measuring graph structures. In this paper, we characterize polygonal chains with the minimum…
We present a novel method for computing reachability probabilities of parametric discrete-time Markov chains whose transition probabilities are fractions of polynomials over a set of parameters. Our algorithm is based on two key…