Let Wn = K1 ∨ Cn−1 be the wheel graph on n vertices, and let S(n, c, k) be the graph on n vertices obtained by attaching n− 2c− 2k − 1 pendant edges together with k hanging paths of length two at vertex v0, where v0 is the unique common vertex of c triangles. In this paper we show that S(n, c, k) (c > 1, k > 1) and Wn are determined by their signless Laplacian spectra, respectively. Moreover, w...

In this paper, we introduce the atom bond connectivity E-Banhatti index and sum of a graph. Also compute these newly defined indices for wheel graphs, friendship chain silicate networks, honeycomb networks nanotubes.

The metric dimension dim(G) of a graph G is the minimum number of vertices such that every vertex of G is uniquely determined by its vector of distances to the chosen vertices. The zero forcing number Z(G) of a graph G is the minimum cardinality of a set S of black vertices (whereas vertices in V (G)\S are colored white) such that V (G) is converted entirely to black after finitely many applica...

OF THE DISSERTATION Explicit Bases of Motives over Number Fields with Application to Feynman Integrals by Yu, Yang Doctor of Philosophy in Mathematics, Washington University in St. Louis, 2016. Professor Matthew Kerr, Chair Let K∗(k) be the algebraic K-theory of a number field k and MT (k) the Tannakian category of mixed Tate motives over k. Then ExtMT (k)(Q(0),Q(n)) = K2n−1(k) ⊗ Q. Periods of ...

A flower is a coin graph representation of the wheel graph. A petal of a flower is an outer coin connected to the center coin. The results of this paper are twofold. First we derive a parametrization of all the rational (and hence integer) radii coins of the 3-petal flower, also known as Apollonian circles or Soddy circles. Secondly we consider a general n-petal flower and show there is a uniqu...

Using graph products we present an O(|V ||E| + |V | log |V |) separation algorithm for the nonsimple 1-wheel inequalities by Cheng and Cunningham (1997) of the stable set polytope, which is faster than their O(|V |) algorithm. There are two ingredients for our algorithm. The main improvement stems from a reduction of separation problem to multiple shortest path problems in an auxillary graph ha...

Abstract An odd wheel graph is a formed by connecting new vertex to all vertices of an cycle. We answer question Rosenfeld and Le showing that wheels cannot be drawn in the plane so lengths edges are integers.

A new graph invariant called the secure vertex cover pebbling number, which is a combination of two invariants, namely, ‘secure cover’ and ‘cover number’, introduced in this paper. The number graph, [Formula: see text], minimum text] so that every distribution pebbles can reach some by sequence moves. In paper, complexity problem are discussed. Also, we obtain basic results for complete text]-p...