15 papers
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…
Khayyam-Pascal Determinantal Arrays, Star of David Rule and Log-Concavity
Hossein Teimoori Faal, Hasan Khodakarami
In this paper we develop a new geometric method to answer the log-concavity questions related to a nice class of combinatorial sequences arising from the Pascal triangle.
On Gosper-Karaji algebraic Identities
Hossein Teimoori Faal
In this paper, we first quickly review the basics of an algebro-geometric method of Karaji's L-summing technique in today's modern language of algebra. Then, we also review the the…
Maximum Independent Set of Cliques and The Generalized Mantel's Theorem
Hossein Teimoori Faal
A complete subgraph of any simple graph on vertices is called a -\emph{clique} of . In this paper, we first introduce the concept of the value of a -clique ()…
On Clique Version of the Randic Index
Hossein Teimoori Faal
In this paper, we first review the weighted-versiion of the handshaking lemma based on the idea of a weighted vertex-edge incidence matrix of a given graph . Then, we obtain a g…
On Vertically-Recurrent Matrices and Their Algebraic Properties
Hossein Teimoori Faal
In this paper, we first introduce the new class of vertically-recurrent matrices, using a generalization of "the Hockey stick and Puck theorem" in Pascal's triangle. Then, we give…
Clique Polynomials and Chordal Graphs
Hossein Teimoori Faal
The ordinary generating function of the number of complete subgraphs of is called a clique polynomial of and is denoted by . A real root of is called a cli…
A Multiset Version of Even-Odd Permutations Identity
Hossein Teimoori Faal
In this paper, we give a new bijective proof of a multiset analogue of even-odd permutations identity. This multiset version is equivalent to the original coin arrangements lemma w…
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…
A Generalization of Tepper's Identity
Mortaza Bayat, Hossein Teimoori Faal
In this paper, we first give a simple combinatorial proof of Tepper's identity. Then, as a by product of this interesting identity we present another proof of the well-known Wilson…
Sums of Polynomials and Clique Roots
Hossein Teimoori Faal
In this paper, pursuing the same line of ideas in the proof of an old longstanding open conjecture of \emph{Kadison-Singer} , we introduce a key lemma which we call it the interlac…
On Clique Roots of Flat Graphs
Hossein Teimoori Faal
A complete subgraph of a given graph is called a clique. A clique Polynomial of a graph is a generating function of the number of cliques in . A real root of the clique polynomi…