Forbidden Subposets in the Cycle Poset Aysan Behnia, G. Fath-Tabar, G. Katona Order, 2025 Abstract The cycle poset consists of the intervals of the cyclic permutation of the elements 1, 2, ... , n , ordered by inclusion. Suppose that F is a set of such intervals, none of them is a less than s others. The maximum size of F is determined under this condition. It is also shown that if the largest size of a set in this poset without containing a small subposet P is known, it solves the same problem, up to an additive constant, in the grid poset consisting of the pairs $$(i,j) (1\le i,j\le n)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>i</mml:mi> <mml:mo>,</mml:mo> <mml:mi>j</mml:mi> <mml:mo>)</mml:mo> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>i</mml:mi> <mml:mo>,</mml:mo> <mml:mi>j</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and ordered coordinate-wise.
On the Volume of µ-Way S(K1,3)-Trade on (3, 6)-Fullerene Graphs , Meysam Taheri-Dehkordi, Gholam Hossein Fath-Tabar, and Match, 2025 A perfect star packing in a fullerene graph is a spanning subgraph whose every component is isomorphic to the star graph K1,3. A perfect star packing in a (3, 6)-fullerene graph is called a perfect star packing of type T0 if no center of a star is on a triangle of G. A µ-way G-trade consists of µ disjoint decomposition of graph H into copies of graph G. In this paper, we use the concept of packing and specify values of the number of copies of G=S(K1,3) for which there exists a µ-way S(K1,3)-trade when the underlying graph is a non-trivial (3, 6)-fullerene graph.
G-GRAPH AND Ḡ-GYRO-GRAPH Farzaneh Gholaminezhad, Neda Moradi, Gholam Hossein Fath-Tabar, Alain Bretto Aapp Atti Della Accademia Peloritana Dei Pericolanti Classe Di Scienze Fisiche Matematiche E Naturali, 2025 International audience
Estrada and L-Estrada Indices of a Graph and Their Relationship with the Number of Spanning Trees Mahsa Arabzadeh, , Gholam Hossein Fath-Tabar, Hamid Rasoli, Abolfazl Tehranian, , , and Match, 2023 Let G be a n-vertex simple graph.Suppose A(G) and L(G) = ∆(G) -A(G) are adjacency and Laplacian matrix of G, respectively, where ∆(G) is degree matrix of G. EE(G) = n i=1 e λ i and LEE(G) = n i=1 e µ i are called Estrada and Laplacian Estrada index of G, where λi and µi, 1 ≤ i ≤ n, denote the eigenvalues of A(G) and L(G).In this paper, some new upper and lower bounds for EE(G) and LEE(G) are given.Moreover, some relations between EE(G) and
