The mixed metric dimension of flower snarks and wheels

关于奇环图（snarks）的最小顶点覆盖

On the minimum vertex cover of snarks

本研究针对奇环图，证明判定其是否存在指定大小顶点覆盖为NP完全问题，并确定了多个奇环图子类的顶点覆盖数。

关于顶点集的度量维数

On the Metric Dimensions for Sets of Vertices

本文研究图的多顶点定位问题，提出$\u2113$-实心分辨集概念，建立其与$\u300a\u2113\u3009$-分辨集的关联，给出车图$\u300a2\u3009$-分辨集与区组设计的联系，并借助计算机辅助方法得到花斯诺克图族的相关度量维数结果。

On Hypohamiltonian Snarks and a Theorem of Fiorini

We discuss an omission in the statement and proof of Fiorini's 1983 theorem on hypohamiltonian snarks and present a version of this theorem which is more general in several ways. Using Fiorini's erroneous result, Steffen showed that hypohamiltonian snarks exist for some $n \ge 10$ and each even $n \ge 92$. We rectify Steffen's proof by providing a correct demonstration of a technical lemma on flower snarks, which might be of separate interest. We then strengthen Steffen's theorem to the strongest possible form by determining all orders for which hypohamiltonian snarks exists. This also strengt…

On integer radii coin representations of the wheel graph

A {\em flower} is a coin graph representation of the wheel graph. A {\em petal} of the wheel graph is an edge to the center vertex. In this paper we investigate flowers whose coins have integer radii. For an $n$-petaled flower we show there is a unique irreducible polynomial $P_n$ in $n$ variables over the integers $\ints$, the affine variety of which contains the cosines of the internal angles formed by the petals of the flower. We also establish a recursion that these irreducible polynomials satisfy. Using the polynomials $P_n$, we develop a parameterization for all the integer radii of the …

若干轮相关图与星图张量积的反魔幻性

Antimagicness of Tensor product for some wheel related graphs with star

本文研究连通图反魔幻标号猜想，证明轮、舵图和花图分别与星图作张量积所得图均为反魔幻图。