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Small InducedUniversal Graphs and Compact Implicit Graph Representations
 In Proc. 43’rd annual IEEE Symp. on Foundations of Computer Science
, 2002
"... We show that there exists a graph G with n 2 nodes, where any forest with n nodes is a nodeinduced subgraph of G. Furthermore, the result implies existence of a graph with n nodes that contains all nnode graphs of fixed arboricity k as nodeinduced subgraphs. We provide a lower bound ..."
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of the size of such a graph. The upper bound is obtained through a simple labeling scheme for parent queries in rooted trees.
Labeling Schemes for Bounded Degree Graphs
, 2014
"... We investigate adjacency labeling schemes for graphs of bounded degree ∆ = O(1). In particular, we present an optimal (up to an additive constant) log n+ O(1) adjacency labeling scheme for bounded degree trees. The latter scheme is derived from a labeling scheme for bounded degree outerplanar graph ..."
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We investigate adjacency labeling schemes for graphs of bounded degree ∆ = O(1). In particular, we present an optimal (up to an additive constant) log n+ O(1) adjacency labeling scheme for bounded degree trees. The latter scheme is derived from a labeling scheme for bounded degree outerplanar
Chapter 14 Labeling Schemes
"... Imagine you want to repeatedly query a huge graph, e.g., a social or a road network. For example, you might need to find out whether two nodes are connected, or what the distance between two nodes is. Since the graph is so large, you distribute it among multiple servers in your data center. 14.1 Adj ..."
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. The label of each node u consists of two parts: The ID of u (from 1 to n), and the ID of u’s parent (or nothing if u is the root). Remarks: • What we have constructed above is called a labeling scheme, more precisely a labeling scheme for adjacency in trees. Formally, a labeling scheme is defined as follows
Chapter 14 Labeling Schemes
"... Imagine you want to repeatedly query a huge graph, e.g., a social or a road network. For example, you might need to find out whether two nodes are connected, or what the distance between two nodes is. Since the graph is so large, you distribute it among multiple servers in your data center. 14.1 Adj ..."
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. The label of each node u consists of two parts: The ID of u (from 1 to n), and the ID of u’s parent (or nothing if u is the root). Remarks: • What we have constructed above is called a labeling scheme, more precisely a labeling scheme for adjacency in trees. Formally, a labeling scheme is defined as follows
Adjacency Matrices
 SIAM J. ALG. DISC. METHODS
, 1986
"... For a graph G with vertex set V an algebra of adjacency matrices is defined and viewed as an equivalence relation on V V with certain nice properties. This can be used in algorithms to find automorphisms of graphs and isomorphisms between graphs. It also provides intersection numbers independent of ..."
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For a graph G with vertex set V an algebra of adjacency matrices is defined and viewed as an equivalence relation on V V with certain nice properties. This can be used in algorithms to find automorphisms of graphs and isomorphisms between graphs. It also provides intersection numbers independent
On Randomized Representations of Graphs Using Short Labels
 in "Proc. 21st ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)", 2009, p. 131137 IL
"... Informative labeling schemes consist in labeling the nodes of graphs so that queries regarding any two nodes (e.g., are the two nodes adjacent?) can be answered by inspecting merely the labels of the corresponding nodes. Typically, the main goal of such schemes is to minimize the label size, that is ..."
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by relations between such schemes and other important notions such as universal graphs, extensive research has been made by the community to further reduce the label sizes of such schemes as much as possible. The current state of the art adjacency labeling scheme for trees has label size log n + O(log ∗ n
Labeling
"... A bottomup approach to multiplelevel logic synthesis for lookup table based FPGAs PROEFSCHRIFr ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof.dr. M. Rem, voor een commissie aangewezen door het College voor Promoties in het ..."
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A bottomup approach to multiplelevel logic synthesis for lookup table based FPGAs PROEFSCHRIFr ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof.dr. M. Rem, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op
Neighborhood Homogeneous Labelings of Graphs
"... Given a labeling of the vertices and edges of a graph, we define a type of homogeneity that requires that the neighborhood of every vertex contains the same number of each of the labels. This homogeneity constraint is a generalization of regularity – all such graphs are regular. We consider a specif ..."
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Given a labeling of the vertices and edges of a graph, we define a type of homogeneity that requires that the neighborhood of every vertex contains the same number of each of the labels. This homogeneity constraint is a generalization of regularity – all such graphs are regular. We consider a
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