We consider the enumeration of unlabeled directed hypergraphs by using Pólya’s counting theory and Burnside’s counting lemma. Instead of characterizing the cycle index of the permutation group acting on the hyperarc set A, we treat each cycle in the disjoint cycle decomposition of a permutation ρ acting on A as an equivalence class (or orbit) of A under the operation of the group generated by ρ...

Let G1 and G2 be disjoint copies of a graph G, and let f : V (G1) → V (G2) be a function. Then a functigraph C(G, f) = (V,E) has the vertex set V = V (G1) ∪ V (G2) and the edge set E = E(G1) ∪ E(G2) ∪ {uv | u ∈ V (G1), v ∈ V (G2), v = f(u)}. A functigraph is a generalization of a permutation graph (also known as a generalized prism) in the sense of Chartrand and Harary. In this paper, we study ...

the fact that the properties of a molecule are tightly connected to its structural  characteristics  is one of the fundamental concepts in chemistry. in this connection,  graph theory has been successfully applied in developing some relationships between topological indices and some thermodynamic properties. so ,  a novel method for computing the new descriptors to construct a quantitative rela...

Harary’s & Randić’s ideas of “forcing” & “freedom” involve subsets of double bonds of Kekule structure such as to be unique to that Kekule structure. Such forcing sets are argued to be greatly generalizable to deal with various other coverings, and thence forcing seems to be fundamental, and of notable potential utility. Various forcing invariants associated to (molecular) graphs ensue, with il...

In the graph avoidance game two players alternatingly color edges of a graph G in red and in blue respectively. The player who first creates a monochromatic subgraph isomorphic to a forbidden graph F loses. A symmetric strategy of the second player ensures that, independently of the first player’s strategy, the blue and the red subgraph are isomorphic after every round of the game. We address t...

The stability number of a graph G, denoted by α(G), is the cardinality of a stable set of maximum size in G. If α(G − e) > α(G), then e is an α-critical edge, and if μ(G − e) < μ(G), then e is a μ-critical edge, where μ(G) is the cardinality of a maximum matching in G. G is a König-Egerváry graph if its order equals α(G) + μ(G). Beineke, Harary and Plummer have shown that the set of α-critical ...

Abstract: In this study an appropriate computational approach was presented for estimating the boiling temperatures of 41 different types of olefins and their derivatives. Based on the guidelines of this approach, several structural indices related to the organic components were applied using graph theory. Meanwhile, in addition to evaluating the relation between the boiling temperatures of ole...

it is well known that the chemical behavior of a compound is dependent upon the structure of itsmolecules. quantitative structure – activity relationship (qsar) studies and quantitative structure –property relationship (qspr) studies are active areas of chemical research that focus on the nature ofthis dependency. topological indices are the numerical value associated with chemical constitution...

We determine the values of s and t for which there is a coloring of the edges of the complete bipartite graph Ks,t which admits only the identity automorphism. In particular, we show that for a given s with a few small exceptions, there is such a coloring with c colors if and only r ≤ t ≤ cs − r where r = blogc(s − 1)c + 1 if s ≤ c or if s ≥ c + 1 and s ≥ c1+blogc(s−1)c − blogcblogc(s− 1)cc and...

The line-digraph of a digraph D with vertices V , ..... V is the digrah D* obtained from D by associating with each edge of D a vertex of D*, and then directing an edge from vertex (Vi, VYj) of D* to vertex (Vk, Vm) if and only if j = k. This paper extends a characterization given by Harary and Norman for line-digraphs. It is also possible to repeatedly contract vertices of the line-digraph (wi...