# Journal of Prime Research in Mathematics

Journal of Prime Research in Mathematics (JPRM) ISSN: 1817-3462 (Online) 1818-5495 (Print) is an HEC recognized, Scopus indexed, open access journal which provides a plate forum to the international community all over the world to publish their work in mathematical sciences. JPRM is very much focused on timely processed publications keeping in view the high frequency of upcoming new ideas and make those new ideas readily available to our readers from all over the world for free of cost. Starting from 2020, we publish one Volume each year containing four issues in March, June, September and December. The accepted papers will be published online immediate in the running issue. All issues will be gathered in one volume which will be published in December of every year.

Latest Published Articles

### Topology of configuration spaces

JPRM-Vol. 1 (2005), Issue 1, pp. 111 – 117 Open Access Full-Text PDF
Barbu Berceanu

### Extremal and asymptotic properties of irreducible coverings of graphs by cliques

JPRM-Vol. 1 (2005), Issue 1, pp. 101 – 110 Open Access Full-Text PDF
Ioan Tomescu
Abstract: A clique of a graph G is a complete subgraph of $$G$$ which is maximal relatively to set inclusion and a covering C of G consisting of s cliques is an irreducible covering if the union of any $$s − 1$$ cliques from C is a proper subset of the vertex-set of $$G$$. Some discrete optimization problems involve irreducible coverings of graphs: minimization of Boolean functions, minimization of incompletely specified finite automata, finding the chromatic number of a graph. This paper surveys some recent results by the author on the irreducible coverings of graphs by cliques: the recurrence relation and the exponential generating function of the number of irreducible coverings for bipartite graphs, asymptotic behavior of these numbers and of the maximum number of irreducible coverings by cliques of an n-vertex graph as n tends to infinity, extremal graphs of order n for irreducible coverings by $$n − 2$$ and $$n − 3$$ cliques and the structure of irreducible coverings for bipartite and nonbipartite cases. Some conjectures and open problems are proposed.