A polynomial associated with G is defined as t (G, w)= ∑ _ T ∈ T (G) ∏ _ e ∈ E (T) w_e (G)
t (G, w)=∑ T∈ T (G)∏ e∈ E (T) we (G)(T (G) T (G) is the set of spanning trees of G), which is …

Abstract In 1964, Moon extended Cayley's formula to a nice expression of the number of
spanning trees in complete graphs containing any fixed spanning forest. After nearly 60 …

In chemical graph theory, many topological indices of the hexagonal chains, for instance, the
energy, Wiener and Kirchhoff indices, and numbers of Kekulé structures and spanning trees …

In chemical graph theory, various topological indices of the hexagonal lattices such as the
energy, the numbers of perfect matchings and spanning trees, and so on, have been studied …

The past decade has seen growing importance being attached to the Completely
Independent Spanning Trees (CISTs). The CISTs can facilitate many network functionalities …

The calculation of the number of spanning trees in a graph is an important topic in physics
and combinatorics, which has been studied extensively by many mathematicians and …

Suppose is a loopless graph and is the graph obtained from G by subdividing each of its
edges k () times. Let be the set of all spanning trees of G, be the line graph of the graph and …

In the past few years, much importance and attention have been attached to completely
independent spanning trees (CISTs). Many results, such as edge-disjoint Hamilton cycles …

The problem of counting spanning trees of graphs or networks is a fundamental and crucial
area of research in combinatorics, while has numerous important applications in statistical …

Moon's classical result implies that the number of spanning trees of a complete graph K n
with n vertices containing a given spanning forest F equals nc− 2∏ i= 1 cni, where c is the …