On the Crossing Number of the Join of Five Vertex Graph with the Discrete Graph
نویسندگان
چکیده
In this paper, we show the values of crossing numbers for join products of graph G on five vertices with the discrete graph Dn and the path Pn on n vertices. The proof is done with the help of software. The software generates all cyclic permutations for a given number n. For cyclic permutations, P1 – Pm will create a graph in which to calculate the distances between all vertices of the graph. These distances are used in proof of crossing numbers of presented graphs.
منابع مشابه
On the revised edge-Szeged index of graphs
The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2) ), where mu(e|G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of ed...
متن کاملThe automorphism group of the reduced complete-empty $X-$join of graphs
Suppose $X$ is a simple graph. The $X-$join $Gamma$ of a set ofcomplete or empty graphs ${X_x }_{x in V(X)}$ is a simple graph with the following vertex and edge sets:begin{eqnarray*}V(Gamma) &=& {(x,y) | x in V(X) & y inV(X_x) },\ E(Gamma) &=& {(x,y)(x^prime,y^prime) | xx^prime in E(X) or else x = x^prime & yy^prime in E(X_x)}.end{eqnarray*}The $X-$join graph $Gamma$ is said to be re...
متن کاملVector Space semi-Cayley Graphs
The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph ${rm Cay(mathcal{V},S)}$ is a graph with the vertex set the whole vectors of the vector space $mathcal{V}$ and two vectors $v_1,v_2$ join by an edge whenever...
متن کاملOn list vertex 2-arboricity of toroidal graphs without cycles of specific length
The vertex arboricity $rho(G)$ of a graph $G$ is the minimum number of subsets into which the vertex set $V(G)$ can be partitioned so that each subset induces an acyclic graph. A graph $G$ is called list vertex $k$-arborable if for any set $L(v)$ of cardinality at least $k$ at each vertex $v$ of $G$, one can choose a color for each $v$ from its list $L(v)$ so that the subgraph induced by ev...
متن کاملOn common neighborhood graphs II
Let G be a simple graph with vertex set V (G). The common neighborhood graph or congraph of G, denoted by con(G), is a graph with vertex set V (G), in which two vertices are adjacent if and only if they have at least one common neighbor in G. We compute the congraphs of some composite graphs. Using these results, the congraphs of several special graphs are determined.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017