کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4598735 | 1631098 | 2016 | 21 صفحه PDF | دانلود رایگان |
We explore the concept of a graph homomorphism through the lens of C⁎-algebras and operator systems. We start by studying the various notions of a quantum graph homomorphism and examine how they are related to each other. We then define and study a C⁎-algebra that encodes all the information about these homomorphisms and establish a connection between computational complexity and the representation of these algebras. We use this C⁎-algebra to define a new quantum chromatic number and establish some basic properties of this number. We then suggest a way of studying these quantum graph homomorphisms using certain completely positive maps and describe their structure. Finally, we use these completely positive maps to define the notion of a “quantum” core of a graph.
Journal: Linear Algebra and its Applications - Volume 497, 15 May 2016, Pages 23–43