Clique complexes and graph powers
Michal Adamaszek
TL;DR
This paper investigates how clique complexes of graphs change when graph powers are taken, with specific calculations for powers of cycles and their relation to independence complexes of circular complete graphs.
Contribution
It provides new insights into the behavior of clique complexes under graph power operations, including explicit computations for cycles.
Findings
Clique complexes of powers of cycles are characterized.
Clique complexes relate to independence complexes of circular complete graphs.
New computational methods for these complexes are introduced.
Abstract
We study the behaviour of clique complexes of graphs under the operation of taking graph powers. As an example we compute the clique complexes of powers of cycles, or, in other words, the independence complexes of circular complete graphs.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Graph theory and applications · Advanced Combinatorial Mathematics