The visualization of switch networks is a very interesting tool for analysis and verification of logic cells generated automatically. In this context, the use of graph theory is very useful to attain this objective. The proposed algorithm satisfies this necessity to represent complementary series/parallel and partially “bridge” network logic styles, avoiding any wire crossing. A tool prototype ...

In this paper, subgraphs and complementary graphs are used to analyze the network synchronizability. Some sharp and attainable bounds are provided for the eigenratio of the network structural matrix, which characterizes the network synchronizability, especially when the network’s corresponding graph has cycles, chains, bipartite graphs or product graphs as its subgraphs.

Let γt(G) denote the total domination number of the graph G. G is said to be total domination edge critical, or simply γt-critical, if γt(G+ e) < γt(G) for each edge e ∈ E(G). In this paper we study a family H of 4-critical graphs with diameter three, in which every vertex is a diametrical vertex, and every diametrical pair dominates the graph. We also generalize the self-complementary graphs, ...

We show that for every admissible order v ≡ 0 or 2 (mod 6) there exists a near-Steiner triple system of order v that can be halved. As a corollary we obtain that a Steiner almost self-complementary graph with n vertices exists if and only if n ≡ 0 or 2 (mod 6). © 2008 Elsevier B.V. All rights reserved.

In a currently ongoing project, we investigate a new possibility for solving the k-labelled spanning forest (kLSF) problem by an intelligent Variable Neighbourhood Search (Int-VNS) metaheuristic. In the kLSF problem we are given an undirected input graph G = (V, E, L) where V is the set of nodes, E the set of edges, that are labelled on the set L of labels, and an integer positive value ¯ k, an...

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This paper studies learning node representations with graph neural networks (GNNs) for unsupervised scenario. Specifically, we derive a theoretical analysis and provide an empirical demonstration about the non-steady performance of GNNs over different datasets, when supervision signals are not appropriately defined. The depends on both feature smoothness locality structure. To smooth discrepanc...

It is shown that if L and D are the Laplacian matrix and the distance matrix of a tree respectively, then any minor of the Laplacian equals the sum of the cofactors of the complementary submatrix of D, upto a sign and a power of 2. An analogous, more general result is proved for the Laplacian and the resistance matrix of any graph. A similar identity is proved for graphs in which each block is ...

Coecke and Duncan recently introduced a categorical formalisation of the interaction of complementary quantum observables. In this paper we use their diagrammatic language to study graph states, a computationally interesting class of quantum states. We give a graphical proof of the fixpoint property of graph states. We then introduce a new equation, for the Euler decomposition of the Hadamard g...

A vertex-colored graph G is rainbow vertex-connected if two vertices are connected by a path whose internal vertices have distinct colors. The rainbow vertex-connection number of a connected graph G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertex-connected. If for every pair u, v of distinct vertices, G contains a vertex-rainbow u−v geodesi...