Related papers: Graph diameter, eigenvalues, and minimum-time cons…

The present paper investigates the robustness of the consensus protocol over weighted directed graphs using the Nyquist criterion. The limit to which a single weight can vary, while consensus among the agents can be achieved, is explicitly…

Suppose in a graph $G$ vertices can be either red or blue. Let $k$ be odd. At each time step, each vertex $v$ in $G$ polls $k$ random neighbours and takes the majority colour. If it doesn't have $k$ neighbours, it simply polls all of them,…

The bloom of complex network study, in particular, with respect to scale-free ones, is considerably triggering the research of scale-free graph itself. Therefore, a great number of interesting results have been reported in the past,…

This survey paper deals with upper and lower bounds on the number of $k$-matchings in regular graphs on $N$ vertices. For the upper bounds we recall the upper matching conjecture which is known to hold for perfect matchings. For the lower…

We give an extension of the $G$ method, with results, the extension and results being partly suggested by the finite Markov chains and specially by the finite-time consensus problem for the DeGroot model and that for the DeGroot model on…

Let G be an edge weighted undirected graph. For every pair of nodes consider the shortest cycle containing these nodes in G. The cycle diameter of G is the maximum length of a cycle in this set. Let H be a directed graph obtained by…

We propose consensus propagation, an asynchronous distributed protocol for averaging numbers across a network. We establish convergence, characterize the convergence rate for regular graphs, and demonstrate that the protocol exhibits better…

Let $G$ be a simple connected graph, and $D(G)$ be the distance matrix of $G$. Suppose that $D_{\max}(G)$ and $\lambda_1(G)$ are the maximum row sum and the spectral radius of $D(G)$, respectively. In this paper, we give a lower bound for…

We revisit the classical question of the relationship between the diameter of a graph and its expansion properties. One direction is well understood: expander graphs exhibit essentially the lowest possible diameter. We focus on the reverse…

Erd\H{o}s, Pach, Pollack, and Tuza [\textit{J. Combin. Theory Ser. B, 47(1) (1989), 73-79}] proved that the diameter of a connected $n$-vertex graph with minimum degree $\delta$ is at most $\frac{3n}{\delta+1}+O(1)$. The oriented diameter…

We consider the convergence time for solving the binary consensus problem using the interval consensus algorithm proposed by B\' en\' ezit, Thiran and Vetterli (2009). In the binary consensus problem, each node initially holds one of two…

This paper consider a standard consensus algorithm under output saturations. In the presence of output saturations, global consensus can not be realized due to the existence of stable, unachievable equilibrium points for the consensus.…

Aldous and Fill (2002) conjectured that the maximum relaxation time for the random walk on a connected regular graph with $n$ vertices is $(1+o(1)) \frac{3n^{2}}{2\pi ^{2}}$. A conjecture by Guiduli and Mohar (1996) predicts the structure…

The constrained consensus problem considered in this paper, denoted interval consensus, is characterized by the fact that each agent can impose a lower and upper bound on the achievable consensus value. Such constraints can be encoded in…

Classical approaches for asymptotic convergence to the global average in a distributed fashion typically assume timely and reliable exchange of information between neighboring components of a given multi-component system. These assumptions…

We establish average consensus on graphs with dynamic topologies prescribed by evolutionary games among strategic agents. Each agent possesses a private reward function and dynamically decides whether to create new links and/or whether to…

Let $G$ be a graph and ${\mathcal{\tau}}: V(G)\rightarrow \Bbb{N}\cup \{0\}$ be an assignment of thresholds to the vertices of $G$. A subset of vertices $D$ is said to be a dynamic monopoly corresponding to $(G, \tau)$ if the vertices of…

This research focuses on analyzing the depth of generalized binomial edge ideals. We extend the notion of $d$-compatible map for the pairs of a complete graph and an arbitrary graph, and using it, we give a combinatorial lower bound for the…

This paper studies distributed strategies for average-consensus of arbitrary vectors in the presence of network interference. We assume that the underlying communication on any \emph{link} suffers from \emph{additive interference} caused…

A graph $G$ is $\textit{universal}$ for a (finite) family $\mathcal{H}$ of graphs if every $H \in \mathcal{H}$ is a subgraph of $G$. For a given family $\mathcal{H}$, the goal is to determine the smallest number of edges an…