The real vector space of non-oriented graphs is known to carry a differential graded Lie algebra structure. Cocycles in the Kontsevich graph complex, expressed using formal sums on $n$ vertices and $2n-2$ edges, induce -- under orientation mapping infinitesimal symmetries classical Poisson structures arbitrary finite-dimensional affine manifolds. Willwacher has stated existence nontrivial cocyc...

Let G1 and G2 be two given graphs. The Ramsey number R(G1,G2) is the least integer r such that for every graph G on r vertices, either G contains a G1 or G contains a G2. A complete bipartite graph K1,n is called a star. The kipas ̂ Kn is the graph obtained from a path of order n by adding a new vertex and joining it to all the vertices of the path. Alternatively, a kipas is a wheel with one edg...

The fixation probability of a mutant in the evolutionary dynamics of Moran process is calculated by the Monte-Carlo method on a few families of clique-based graphs. It is shown that the complete suppression of fixation can be realized with the generalized clique-wheel graph in the limit of small wheel-clique ratio and infinite size. The family of clique-star is an amplifier, and clique-arms gra...

In this paper, it is explicitly determined the r-dynamic chromatic number of direct product any given path with either a complete graph or wheel graph. Illustrative examples are shown for each one cases that studied throughout paper.

We characterize all of the ways to represent the wheel matroids and whirl matroids using frame matroids of signed graphs. The characterization of wheels is in terms of topological duality in the projective plane and the characterization of whirls is in terms of topological duality in the annulus.

Abstract In this paper, the exact formulae for the Harary indices of join, disjunction, symmetric difference, strong product of graphs are obtained. Also, the Schultz and modified Schultz indices of join and strong product of graphs are computed. We apply some of our results to compute the Harary, Schultz and modified Schultz indices of fan graph, wheel graph, open fence and closed fence graphs.

The mod sum number p( G) of a connected graph G is the minimum number of isolated vertices required to transform G into a mod sum graph. It is known that the mod sum number is greater than zero for wheels, Wn, when n > 4 and for the complete graphs, Kn when n 2: 2. In this paper we show that p( Hm,n) > 0 for n > m ;::: 3. Vie show further that P(K2) = P(K3) = 1 while p(Kn) = n for n ;::: 4. We ...

In this paper, we focus on calculate the number of spanning trees general wheel graphs, which meansthe original graphs adding large amount vertices and edges. Particularly, introduce C-graphand deduce a new equation that computing by removing C-graphs instead edges.In Addition, test our results Kirchhoff’s matrix-tree theorem in some simple cases provide thetree entropy graphs. Finally, analyse...

A wheel is a graph consisting of an induced cycle length at least four and single additional vertex with three neighbours on the cycle. We prove that no Burling contains wheel. graphs are triangle-free have arbitrarily large chromatic number, so this answers question Trotignon disproves conjecture Scott Seymour.