5 papers · 1 filter
A Bivariate -Restricted Clique Polynomial: From Local Neighborhoods to Global Expansion
Hossein Teimoori Faal
Let be a finite simple graph and . We introduce the \emph{bivariate -restricted clique polynomial} \[ C_B(G;x,y) = \sum_{\substack{K \subseteq V \\ K \text…
A -Restricted Clique Polynomial and Connections to Tanner's Inequality
Hossein Teimoori Faal
Let be a finite simple graph and . We study the \emph{-restricted clique polynomial} , including its weighted version allowing vertex multiplicit…
A Factorization of the Log-Concavity Operator for Pascal Determinantal Arrays and Their Infinite Row-Wise Log-Concavity
Hossein Teimoori Faal, Hasan Khodakarami
We study the Pascal determinantal arrays $\PD_k$, whose entries $\PD_k(i,j)$ are the minors of the lower-triangular Pascal matrix . We pr…
On Lyndon-Word Representable Graphs
Hossein Teimoori Faal
In this short note, we first associate a new simple undirected graph with a given word over an ordered alphabet of -letters. We will call it the Lyndon graph of that word. Then,…
On Clique Incidence Matrices and Derivatives of Clique Polynomials
Hossein Teimoori Faal
The ordinary generating function of the number of complete subgraphs (cliques) of , denoted by , is called the The clique polynomial of the graph . In this paper, we…