Let $G$ be a simple connected graph and ${v_1,v_2,ldots‎, ‎v_k}$ be the set of‎ ‎pendent (vertices of degree one) vertices of $G$‎. ‎The reduced distance matrix of $G$ is a square matrix whose $(i,j)$-entry is the topological ...

We give a new recursive method to compute the number of cliques and cycles of a graph‎. ‎This method is related‎, ‎respectively to the number of disjoint cliques in the complement graph and to the sum of permanent function ...

The colorful paths and rainbow paths have been considered by several‎ ‎authors‎. ‎A colorful directed path in a digraph $G$ is a directed path with $chi(G)$ vertices whose colors are different‎. ‎A $v$-colorful directed ...

‎‎The Frobenius complement of a given Frobenius group acts on its kernel‎. ‎The scheme which is arisen from the orbitals of this action is called Ferrero pair scheme‎. ‎In this paper‎, ‎we show that the fibers of a Ferrero ...

In this paper we study the first Zagreb index in bucket recursive trees containing buckets with variable‎ ‎capacities‎. ‎This model was introduced by Kazemi in 2012‎. ‎We‎ ‎obtain the mean and variance of the first Zagreb ...

A modular $k!$-coloring‎, ‎$kge 2,$ of a graph $G$ is a coloring of the vertices of $G$ with the elements in $mathbb{Z}_k$ having the property that for every two adjacent vertices of $G,$ the sums of the colors of their ...