In graph theory, a wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle. A wheel graph with n vertices can also be defined as the 1- skeleton of an (n – 1)-gonal pyramid.

In this paper, we determine and show the proof of the metric dimension of a wheel graph and the partition dimension of graph F = Ks + Kt. The solution for the metric dimension is divided into...

Wheel graphs are graceful (Frucht 1979), self-dual, pancyclic, and dominating unique. The wheel graph has graph dimension 2 for (and hence is unit-distance) and dimension 3 otherwise (and hence not unit-distance) (Erdős et al. 1965, Buckley and Harary 1988). Wheel graphs can be constructed in the Wolfram Language using WheelGraph[n].

Let G G be a graph with L(G) L (G) isomorphic to W6 W 6. Since W6 W 6 has exactly 6 vertices, G G has exactly 6 edges. One vertex in W6 W 6 is adjacent to all 5 other vertices, so one edge e e of G G is adjacent to all 5 other edges of G G.

2021年2月10日 · If we call that $f(x)$ then the chromatic polynomial of $W_6$ (the wheel graph with $6$ vertices) is $xf(x-1)$. Because, if you have $x$ colors available, then there are $x$ ways to color the central vertex, and after you've done that, there are $f(x-1)$ ways to color the rest of the vertices with the other $x-1$ colors. $\endgroup$

在 拟阵 论中，两类重要的拟阵 轮拟阵 （英语： wheel matroids）和 旋拟阵 （英语： whirl matroids）的概念都是轮图的推广。 轮图 W6 是 埃尔德什·帕尔 对 拉姆齐理论 一个猜想的反例：他猜想在色数相同的图中，完全图的拉姆齐数是最小的。 但后来有研究发现 W6 的拉姆齐数是17，而与之色数相同的完全图 K4 的拉姆齐数则是18 [5]。 也就是说，对于任意17节点的图 G， G 或它的补图一定有子图 W6；而17节点的 Paley图（英语：Paley graph） 和它的补图都没有 …

Let the spokes of Wn W n be the edges incident with the vertex of degree n − 1 n − 1 (the hub). Let the rim vertices be the vertices different from the hub. First count the number of Hamiltonian paths having exactly 1 spoke. There are n − 1 n − 1 spokes, and each spoke corresponds to 2 Hamiltonian paths (counterclockwise & clockwise).

Download scientific diagram | W 6 , the oriented wheel graph on 6 vertices from publication: Incidence and Laplacian matrices of wheel graphs and their inverses | It has been an open problem...

In this paper, we determine and show the proof of the metric dimension of a wheel graph and the partition dimension of graph F = Ks + Kt. The solution for the metric dimension is divided into four cases. If n = 3 or 6, the metric dimension of wheel

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