For a set $X$ of binary words of length $h$ the daisy cube $Q_h(X)$ is defined as the subgraph of the hypercube $Q_h$ induced by the set of all vertices on shortest paths that connect vertices of $X$ with the vertex $0 ^h$. A vertex in the intersection of all of these paths is a minimal vertex of a daisy cube. A graph $G$ isomorphic to a daisy cube admits several isometric embeddings into a hypercube. We show that an isometric embedding is proper if and only if the label $0 ^h$ is assigned to a minimal vertex of $G$. This result allows us to devise an algorithm which finds a proper embedding of a graph isomorphic to a daisy cube into a hypercube in linear time.
Resonance graphs of kinky benzenoid systems are daisy cubes
Klavžar和Mollard介绍了雏菊立方体是有趣的等距子图$ n$ -立方体$Q_n$，诱导与间隔之间的极大元偏序集$ (V (Q_n),\leq)$和顶点$ 0^n \in V (Q_n)$。本文证明，如果所考虑的分子可以用所谓的kinky苯型体系（即不含线性六边形的亚稠苯型体系）来模拟，则反映芳烃分子Kekulé结构之间相互作用的共振图是一个雏菊立方体。
Penn State University（宾夕法尼亚州立大学）；University of Maribor, Faculty of Natural Sciences and Mathematics（马里博尔大学自然科学与数学学院）；Institute of Mathematics, Physics and Mechanics（数学、物理与力学研究所）；University of Maribor, Faculty of Chemistry and Chemical Engineering（马里博尔大学化学与化学工程学院）
Resonance graphs that are daisy cubes: from hypercubes to independent sets via resonant sets
Faculty of Mechanical Engineering, University of Ljubljana（卢布尔雅那大学机械工程学院）；Institute of Mathematics, Physics and Mechanics, Ljubljana（卢布尔雅那大学数学物理力学研究所）；Department of Mathematics, Penn State University Beaver Campus（宾夕法尼亚州立大学比弗分校数学系）；Faculty of Natural Sciences and Mathematics, University of Maribor（马里博尔大学自然科学与数学学院）；Faculty of Chemistry and Chemical Engineering, University of Maribor（马里博尔大学化学与化学工程学院）
Lattice coverings by parallelotopes containing cube vertices
Institute of Mathematics and Informatics Bulgarian Academy of Sciences（保加利亚科学院数学与信息学研究所）；Faculty of Information Sciences State University of Library Studies and Information Technologies（图书馆研究与信息技术州立大学信息科学学院）
