A [see formula in PDF]-fullerene is a connected cubic plane graph whose faces are only triangles and hexagons, has the connectivity PDF] or PDF]. The PDF]-fullerenes with tubes consisting of concentric hexagonal layers such that each layer consists two capped on end by adjacent triangles, denoted vertices exactly perfect matchings. structure can be determined three parameters PDF], and[see thus...

Connectivity and edge-connectivity of a graph measure the difficulty of breaking the graph apart, but they are very much affected by local aspects like vertex degree. Average connectivity (and analogously, average edge-connectivity) has been introduced to give a more refined measure of the global “amount” of connectivity. In this paper, we prove a relationship between the average connectivity a...

Matching extendability is significant in graph theory and its applications. The basic notion in this direction is n-extendability introduced by Plummer in 1980. Motivated by the different natures of bipartite matchings and non-bipartite matchings, this paper investigates bipartite-matching extendable (BM-extendable) graphs. A graph G is said to be BM-extendable if every matching M which is a pe...

The Berge–Fulkerson Conjecture states that every cubic bridgeless graph has six perfect matchings such that every edge of the graph is contained in exactly two of these perfect matchings. In this paper, a useful technical lemma is proved that a cubic graph G admits a Berge–Fulkerson coloring if and only if the graph G contains a pair of edge-disjoint matchings M1 and M2 such that (i) M1 ∪ M2 in...