An n-dimensional folded hypercube FQn is an attractive variance of an n-dimensional hypercube Qn, which is obtained by a standard hypercube with some extra edges established between its vertices. FQn for any odd n is known to be bipartite. In this paper, for any FQn (n ≥ 2) with at most 2n−3 faulty edges in which each vertex is incident with at least two fault-free edges, we prove that there ex...

A graph is said to be pancyclic if it contains cycles of every length from its girth to its order inclusive; and a bipartite graph is said to be bipancyclic if it contains cycles of every even length from its girth to its order. The pancyclicity or the bipancyclicity of a given network is an important factor in determining whether the network’s topology can simulate rings of various lengths. An...

Faults in a network may take various forms such as hardware/software errors, vertex/edge faults, etc. Folded hypercube is a well-known variation of the hypercube structure and can be constructed from a hypercube by adding a link to every pair of nodes with complementary addresses. Let FFv (respectively, FFe) be the set of faulty nodes (respectively, faulty links) in an n-dimensional folded hype...

In this manuscript, if a reduced divisor D0 of hyperelliptic curve of genus g over an extension field Fqn is written by a linear sum of ng elements of Fqn -rational points of the hyperelliptic curve whose x-coordinates are in the base field Fq, D0 is noted by a decomposed divisor and the set of such Fqn -rational points is noted by the decomposed factor of D0. We propose an algorithm which chec...

In this paper, we focus on a hypercube-like structure, the folded hypercube, which is basically a standard hypercube with some extra links between its nodes. Let f be a faulty vertex in an n-dimensional folded hypercube FQn. We show that FQn−{f } contains a faultfree cycle of every even length from 4 to 2n−2 if n ≥ 3 and, furthermore, every odd length from n+ 1 to 2n − 1 if n ≥ 2 and n is even....

Motivated by the well-known Paley graphs over finite fields and their generalizations, in this paper we explore a natural multiplicative-additive analogue of such arising from vector spaces fields. Namely, if n≥2 U⊊Fqn is an Fq-vector space, GU (undirected) graph with vertex set V(GU)=Fqn edge E(GU)={(a,b)∈Fqn2|a≠b,ab∈U}. We describe structure arbitrary maximal clique provide bounds on number ω...