A stable (or independent) set in a graph is a set of pairwise non-adjacent vertices. The
stability number α (G) is the size of a maximum stable set in the graph G. There are three …

We give a formula for the v-number of a graded ideal that can be used to compute this
number. Then, we show that for the edge ideal I (G) of a graph G, the induced matching …

We introduce a construction on a flag complex that by means of modifying the associated
graph generates a new flag complex whose h-vector is the face vector of the original …

A graph G is well-covered if all its maximal stable sets have the same size, denoted by α
(G)[MD Plummer, Some covering concepts in graphs, Journal of Combinatorial Theory 8 …

The circulant graph Cn, S is the graph on n vertices (with labels 0, 1, 2,..., n− 1), spread
around a circle, where two vertices u and v are adjacent iff their (minimum) distance| u− v …

Given two graphs G and H, assume that C={C 1, C 2,…, C q} is a clique cover of G and U is a
subset of V (H). We introduce a new graph operation called the clique cover product …

If 𝑠𝑘 equals the number of stable sets of cardinality k in the graph G, then
I\left(G;x\right)=∑k=0^α\left(G\right)s_kx^k is the independence polynomial of G (Gutman …

In 1987, Alavi, Malde, Schwenk and Erdős conjectured that the independence polynomial of
any tree is unimodal. Although it attracts many researchers' attention, it is still open …

If s κ denotes the number of stable sets of cardinality κ in the graph G, then I (G; x)= ∑ k= 0^
α s_k x^ k is the independence polynomial of G (Gutman, Harary, 1983), where α= α (G) is …

An independent set in a graph G is a set of pairwise non-adjacent vertices. Let ik (G) denote
the number of independent sets of cardinality k in G. Then, its generating function I (G; x)=∑ …