ar X iv : 1 51 1 . 05 00 9 v 1 [ m at h . C O ] 1 6 N ov 2 01 5 What Graphs are 2 - Dot Product Graphs ? ⋆
نویسندگان
چکیده
Let d ≥ 1 be an integer. From a set of d-dimensional vectors, we obtain a d-dot product graph by letting each vector au correspond to a vertex u and by adding an edge between two vertices u and v if and only if their dot product au · av ≥ t, for some fixed, positive threshold t. Dot product graphs can be used to model social networks. Recognizing a d-dot product graph is known to be NP-hard for all fixed d ≥ 2. To understand the position of d-dot product graphs in the landscape of graph classes, we consider the case d = 2, and investigate how 2-dot product graphs relate to a number of other known graph classes.
منابع مشابه
ar X iv : m at h / 04 05 17 6 v 3 [ m at h . R T ] 1 7 N ov 2 00 4 QUANTIZED SYMPLECTIC OSCILLATOR ALGEBRAS OF RANK ONE
A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with Uq(sl2). We study its representation theory, and in particular, its category O.
متن کاملar X iv : m at h / 06 11 62 6 v 1 [ m at h . C O ] 2 1 N ov 2 00 6 COUNTING LINKS IN COMPLETE GRAPHS
We find the minimal number of links in an embedding of any complete k-partite graph on 7 vertices (including K 7 , which has at least 21 links). We give either exact values or upper and lower bounds for the minimal number of links for all complete k-partite graphs on 8 vertices. We also look at larger complete bipartite graphs, and state a conjecture relating minimal linking embeddings with min...
متن کاملar X iv : m at h / 99 11 07 4 v 1 [ m at h . Q A ] 1 1 N ov 1 99 9 CRYSTAL GRAPHS FOR BASIC REPRESENTATIONS OF THE QUANTUM AFFINE
We give a realization of crystal graphs for basic representations of the quantum affine algebra Uq(C (1) 2) in terms of new combinatorial objects called the Young walls.
متن کامل