In this paper we survey and put in a common framework several works that have been
developed in different contexts, all dealing with the same abstract problem, called …

Motivated by a relaxed notion of the celebrated Hamiltonian cycle, this paper investigates its
variant, parity Hamiltonian cycle (PHC): A PHC of a graph is a closed walk which visits every …

We discuss functions from edges and vertices of an undirected graph to an Abelian group.
Such functions, when the sum of their values along any cycle is zero, are called balanced …

This paper investigates a variant of the Hamiltonian cycle, the parity Hamiltonian cycle
(PHC) problem: a PHC in a directed graph is a closed walk (possibly using an arc more than …

A group valued function on a graph is called balanced if the product of its values along any
cycle is equal to the identity element of the group. We compute the number of balanced …

The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is
consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya …

We discuss functions from the edges and vertices of a directed graph to an Abelian group.
Such functions, when the sum of their values along any cycle is zero, are called balanced …

Abstract Let G=(V, E) be an undirected graph with possible multiple edges and loops (a
multigraph). Let A be an Abelian group. In this work we study the following topics: 1) A …

A group-valued function on a graph is called balanced if the product of its values along any
cycle is equal to the identity element of the group. Such functions themselves form a group …

It was 1971 when the notion of NP-completeness was introduced by Cook. Karp proposed
21 NP-complete problems, and more than half of them are graph problems, including …