Related papers: Kirchhoff's Circuit Law Applications to Graph Simp…
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…
In general the problem of finding a miminum spanning tree for a weighted directed graph is difficult but solvable. There are a lot of differences between problems for directed and undirected graphs, therefore the algorithms for undirected…
A solution to a problem of Erd\H{o}s, Rubin and Taylor is obtained by showing that if a graph $G$ is $(a:b)$-choosable, and $c/d > a/b$, then $G$ is not necessarily $(c:d)$-choosable. The simplest case of another problem, stated by the same…
Driven by many applications in graph analytics, the problem of computing $k$-edge connected components ($k$-ECCs) of a graph $G$ for a user-given $k$ has been extensively studied recently. In this paper, we investigate the problem of…
We provide algorithms involving edge slides, for a connected simple graph to evolve in a finite number of steps to another connected simple graph in a prescribed configuration, and for the regularization of such a graph by the minimization…
We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification…
The guessing number of a directed graph (digraph), equivalent to the entropy of that digraph, was introduced as a direct criterion on the solvability of a network coding instance. This paper makes two contributions on the guessing number.…
We consider the problem of finding a "fair" meeting place when S people want to get together. Specifically, we will consider the cases where a "fair" meeting place is defined to be either 1) a node on a graph that minimizes the maximum…
We consider the worst-case query complexity of some variants of certain \cl{PPAD}-complete search problems. Suppose we are given a graph $G$ and a vertex $s \in V(G)$. We denote the directed graph obtained from $G$ by directing all edges in…
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…
The fundamental theory of energy networks in different energy forms is established following an in-depth analysis of the nature of energy for comprehensive energy utilization. The definition of an energy network is given. Combining the…
A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that…
This paper will contribute to a practical problem, Urban Traffic. We will investigate those features, try to simplify the complexity and formulize this dynamic system. These contents mainly contain how to analyze a decision problem with…
Coloring problems in graphs have been used to model a wide range of real applications. In particular, the List Coloring Problem generalizes the well-known Graph Coloring Problem for which many exact algorithms have been developed. In this…
Handwritten circuit diagrams from educational scenarios or historic sources usually exist on analogue media. For deriving their functional principles or flaws automatically, they need to be digitized, extracting their electrical graph.…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…
In this paper, we study the redundancy of linear codes with graph constraints. First we consider linear parity check codes based on bipartite graphs with diversity and with generalized graph constraints. We describe sufficient conditions on…
Given a graph $M,$ path eigenvalues are eigenvalues of its path matrix. The path energy of a simple graph $M$ is equal to the sum of the absolute values of the path eigenvalues of the graph $M$ (Shikare et. al, 2018). We have discovered new…
Through legislation and technical advances users gain more control over how their data is processed, and they expect online services to respect their privacy choices and preferences. However, data may be processed for many different…