In this paper we define the removable cycle that, if $Im$ is a class of graphs, $Gin Im$, the cycle $C$ in $G$ is called removable if $G-E(C)in Im$. The removable cycles in Eulerian graphs have been studied. We characterize Eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for Eulerian graph to have removable cycles h...

The concepts of covering and matching in fuzzy graphs using strong arcs are introduced and obtained the relationship between them analogous to Gallai’s results in graphs. The notion of paired domination in fuzzy graphs using strong arcs is also studied. The strong paired domination number γspr of complete fuzzy graph and complete bipartite fuzzy graph is determined and obtained bounds for the s...

‎let $r$ be a commutative ring with non-zero identity. ‎we describe all $c_3$‎- ‎and $c_4$-free intersection graph of non-trivial ideals of $r$ as well as $c_n$-free intersection graph when $r$ is a reduced ring. ‎also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎finally, ‎we shall prove that almost all artin rings $r$ have hamiltonian intersection graphs. ...

In this paper, we introduce a family of graphs which is a generalization of zero-divisor graphs and compute an upper-bound for the diameter of such graphs. We also investigate their cycles and cores

In this paper, we determine the degree distance of the complement of arbitrary Mycielskian graphs. It is well known that almost all graphs have diameter two. We determine this graphical invariant for the Mycielskian of graphs with diameter two.

In two recent publications [1] Graovac and Trinajstic developed the graph-theoretical description of the Möbius-type conjugated systems. For the role which the Möbius strip concept plays in the chemistry of annulenes and in the theory of the electrocyclic closures, see [1] and the papers cited therein. Möbius graphs differ from simple molecular graphs (also called [1] Hückel graphs) in having a...

The Hosoya index Z(G) of a graph G is defined as the total number of edge independent sets of G. In this paper, we extend the research of [J. Ou, On extremal unicyclic molecular graphs with maximal Hosoya index, Discrete Appl. Math. 157 (2009) 391–397.] and [Y. Ye, X. Pan, H. Liu, Ordering unicyclic graphs with respect to Hosoya indices and Merrifield-Simmons indices, MATCH Commun. Math. Comput...

Most of the molecular graphs in area mathematical chemistry are irregular. Therefore, irregularity measure is a crucial parameter chemical graph theory. One such that has recently been proposed ve-degree index (irrve). Quantitative structure property relationship (QSPR) analysis explores capability an to model numerous properties molecules. We investigate usefulness irrve predicting different p...

Molecules and molecular compounds are often modeled by molecular graphs. One of the most widely known topological descriptor [6, 9] is the Wiener index named after chemist Harold Wiener [13]. The Wiener index of a graph G(V, E) is defined as W (G) = ∑ u,v∈V d(u, v), where d(u, v) is the distance between vertices u and v (minimum number of edges between u and v). A majority of the chemical appli...

The function of enzymes as well as the function of proteins involved in regulatory pathways often implies interactions with small chemical compounds. To understand the function of these proteins as well as for applications such as predicting activity or adverse effects of potential drugs we try here to compute the similarity between chemical compounds using a new similarity function based on th...