Related papers: The Cut Method on Hypergraphs for the Wiener Index

The Wiener index of a connected graph is the summation of all distances between unordered pairs of vertices of the graph. In this paper, we give an upper bound on the Wiener index of a $k$-connected graph $G$ of order $n$ for integers…

In this paper we obtain bounds on a very general class of distance-based topological indices of graphs, which includes the Wiener index, defined as the sum of the distances between all pairs of vertices of the graph, and most…

Let $\mathcal{H}$ be a hypergraph on the non-empty finite vertex set $V(\mathcal{H})$ with the hyperedge set $E(\mathcal{H})$, where each hyperedge $e \in E(\mathcal{H})$ is a subset of $V(\mathcal{H})$ with at least two vertices. This…

Besides the well known Wiener index, which sums up the distances between all the pairs of vertices, and the hyper-Wiener index, which includes also the squares of distances, the edge versions of both indices attracted a lot of attention in…

The Wiener index of a connected graph is the sum of the distance of all pairs of distinct vertices. It was introduced by Wiener in 1947 to analyze some aspects of branching by fitting experimental data for several properties of alkane…

We address counting and optimization variants of multicriteria global min-cut and size-constrained min-$k$-cut in hypergraphs. 1. For an $r$-rank $n$-vertex hypergraph endowed with $t$ hyperedge-cost functions, we show that the number of…

We show that $k$-uniform hypergraphs on $n$ vertices whose codegree is at least $(2/3 + o(1))n$ can be decomposed into tight cycles, subject to the trivial divisibility conditions. As a corollary, we show those graphs contain tight Euler…

In this paper, we investigate how the Wiener index of unicyclic graphs varies with graph operations. These results are used to present a sharp lower bound for the Wiener index of unicyclic graphs of order $n$ with girth and the matching…

The K-way vertex cut problem} consists in, given a graph G, finding a subset of vertices of a given size, whose removal partitions G into the maximum number of connected components. This problem has many applications in several areas. It…

Hypergraphs have gained increasing attention in the machine learning community lately due to their superiority over graphs in capturing super-dyadic interactions among entities. In this work, we propose a novel approach for the partitioning…

In 1997 Klav\v{z}ar and Gutman suggested a generalization of the Wiener index to vertex-weighted graphs. We minimize the Wiener index over the set of trees with the given vertex weights' and degrees' sequences and show an optimal tree to be…

The splitting-off operation in undirected graphs is a fundamental reduction operation that detaches all edges incident to a given vertex and adds new edges between the neighbors of that vertex while preserving their degrees. Lov\'asz (1974)…

The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…

An $r$-cut of a $k$-uniform hypergraph is a partition of its vertex set into $r$ parts, and the size of the cut is the number of edges which have at least one vertex in each part. The study of the possible size of the largest $r$-cut in a…

In this paper, we investigate various algebraic and graph theoretic properties of the distance matrix of a graph. Two graphs are $D$-cospectral if their distance matrices have the same spectrum. We construct infinite pairs of $D$-cospectral…

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…

The Wiener index of a graph is the sum of all pairwise shortest-path distances between its vertices. In this paper we study the novel problem of finding a minimum Wiener connector: given a connected graph $G=(V,E)$ and a set $Q\subseteq V$…

While there have been many results on lower bounds for Max Cut in unweighted graphs, there are only few results for lower bounds for Max Cut in weighted graphs. In this paper, we launch an extensive study of lower bounds for Max Cut in…

Hypergraphs serve as a powerful tool for modeling complex relationships across domains like social networks, transactions, and recommendation systems. The (k,g)-core model effectively identifies cohesive subgraphs by assessing internal…

Wiener index, defined as the sum of distances between all unordered pairs of vertices, is one of the most popular molecular descriptors. It is well known that among 2-vertex connected graphs on $n\ge 3$ vertices, the cycle $C_n$ attains the…