Graph Signal Processing: Foundations and Emerging Directions [From the Guest Editors]
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We define the crossing number for an embedding of a graph G into R^3, and prove a lower bound on it which almost implies the classical crossing lemma. We also give sharp bounds on the space crossing numbers of pseudo-random graphs. ...
This paper introduces the connection-graph-stability method and uses it to establish a new lower bound on the algebraic connectivity of graphs (the second smallest eigenvalue of the Laplacian matrix of the graph) that is sharper than the previously publish ...
Two subsets of vertices in a graph are called homometric if the multisets of distances determined by them are the same. Let h(n) denote the largest number h such that any connected graph of n vertices contains two disjoint homometric subsets of size h. It ...
Artificial neural networks, electronic circuits, and gene networks are some examples of systems that can be modeled as networks, that is, as collections of interconnected nodes. In this paper we introduce the concept of terminal graph (t-graph for short), w ...
Networks are everywhere and we are confronted with many networks in our daily life. Networks such as Internet, World Wide Web, social, biological and economical networks have been subject to extensive studies in the last decade. The volume of publications ...
A drawing of a graph in the plane is called a thrackle if every pair of edges meet precisely once, either at a common vertex or at a proper crossing. According to Conway's conjecture, every thrackle has at most as many edges as vertices. We prove this conj ...
In this work we consider a graph G where a common source sends two messages W1 and W2 to several receivers D1, D2, . . . , DK. The first two receivers D1 and D2 would like to receive message W1, while receivers D3, . . . , DK would like to receive both mes ...
We consider communication of two degraded mes- sage sets over graphs where a common source sends two prioritized messages (a common and a private message) to several receivers. All receivers require the common message and a subset of the receivers require ...
A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum number of edges that a thrackle of n vertices can have. According to a 40 yea ...
The inverse degree of a graph is the sum of the reciprocals of the degrees of its vertices. We prove that in any connected planar graph, the diameter is at most 5/2 times the inverse degree, and that this ratio is tight. To develop a crucial surgery method ...
