Let n 1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1 k n. The hyper-star graph B(n;k) is...

An algebraic distance graph is defined to be a graph with vertices in En in which two vertices are adjacent if and only if the distance between them is an algebraic number. It is proved that an algebraic distance graph with finite vertex set is complete if and only if the graph is "rigid". Applying this result, we prove that ( 1 ) if all the sides of a convex polygon T which is inscribed in a c...

Topolojik indekslerin matematiksel kimyada kulanım alanı bulunmaktadır. Uzaklık-bazlı topolojik ise moleküler graf teoride oldukça önemi vardır. Harary indeksi uzaklık-bazlı bir değişmezidir. Yakın zamanda cebirsel yapı üzerinde nokta çarpım grafı çalışıldı. Bu çalışmada da bu grafın verilecektir.

Throughout this paper, R will denote a commutative ring with identity and M is a unitary R- module and Z will denote the ring of integers. We introduce the graph Ω(M) of module M with the set of vertices contain all nontrivial non-essential submodules of M. We investigate the interplay between graph-theoretic properties of Ω(M) and algebraic properties of M. Also, we assign the values of natura...

Algebraic graph rewriting, which works by first removing the part of the graph to be regarded as garbage, and then gluing in the new part of the graph, is contrasted with term graph rewriting, which works by first gluing in the new part of the graph (the contractum) and performing redirections, and then removing garbage. It is shown that in the algebraic framework these two strategies can be re...