This paper introduces a family of tetravalent graphs called rose window graphs, denoted by Rn(a, r), and investigates their symmetry properties. Four families of these graphs are shown to be edge-transitive and it is conjectured that every Rn(a, r) which is edge-transitive belongs to one of these families. Proofs and conjectures about the size of a dart-stabilizer and about regular maps contain...

If the relation E is transitive, i.e., if (x, y) E E and (y, z) E E imply that (x, z) E E, we speak of a transitive tournament or a total order. Clearly (Z, <) is a total order. We tend to visualize tournaments by considering every edge (x, y) E E as an arrow leading from x to y. In this sense every tournament can also be considered as a complete graph in which every edge is oriented in some di...

this paper is dedicated to propose an algorithm in order to generate the certain isomers of some well-known fullerene bases. furthermore, we enlist the bipartite edge frustration correlated with some of symmetrically distinct in nite families of fullerenes generated by the oered process.

The paper describes a construction of abstract polytopes from Cayley graphs of symmetric groups. Given any connected graph G with p vertices and q edges, we associate with G a Cayley graph G(G) of the symmetric group Sp and then construct a vertex-transitive simple polytope of rank q, the graphicahedron, whose 1-skeleton (edge graph) is G(G). The graphicahedron of a graph G is a generalization ...

the edge szeged index is a new molecular structure descriptor equal to the sum of products mu(e)mv(e) over all edges e = uv of the molecular graph g, where mu(e) is the number of edges which its distance to vertex u is smaller than the distance to vertex v, and nv(e) is defined analogously. in this paper, the edge szeged index of one-pentagonal carbon nanocone cnc5[n] is computed for the first ...

Let X be an in®nite, locally ®nite, almost transitive graph with polynomial growth. We show that such a graph X is the inverse limit of an in®nite sequence of ®nite graphs satisfying growth conditions which are closely related to growth properties of the in®nite graph X. 1991 Mathematics Subject Classi®cation. Primary 05C25, Secondary 20F18 1. Introduction and statement of main result. We think...

In this note we consider two related infinite families of graphs, which generalize the Petersen and the Coxeter graph. The main result proves that these graphs are cores. It is determined which of these graphs are vertex/edge/arc-transitive or distance-regular. Girths and odd girths are computed. A problem on hamiltonicity is posed.

Let $G= (V,E)$ be a $(p,q)$-graph. A bijection $f: Eto{1,2,3,ldots,q }$ is called an edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ where $f^+(u) = sum_{uwin E} f(uw)$. Moreover, a bijection $f: Eto{1,2,3,ldots,q }$ is called a semi-edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ or $f^+(u)=f^+(v)$. A graph that admits an&nbsp; ...

A graph G is balanced if the maximum ratio of edges to vertices, taken over all subgraphs of G, occurs at G itself. This note uses the maxow/min-cut theorem to prove a good characterization of balanced graphs. This characterization is then applied to some results on how balanced graphs may be combined to form a larger balanced graph. In particular, we show that edge-transitive graphs and comple...