Transactions on Combinatorics
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ارسال های اخیر
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$G$-designs for the connected triangular bicyclic graphs with nine edges
(University of Isfahan, 2025-12-01)A $G$-design of order $n$ is a decomposition of the complete graph $K_n$ into isomorphic copies of $G$. We show that if $G$ is a connected bicyclic graph with nine edges containing two triangles, a $G$-design of order $n$ ...
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Three new classes of binomial Fibonacci sums
(University of Isfahan, 2025-12-01)In this paper, we introduce three new classes of binomial sums involving Fibonacci (Lucas) numbers and weighted binomial coefficients. One particular result is linked to a problem proposal recently published in the journal ...
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On twin EP numbers
(University of Isfahan, 2025-12-01)EP numbers were introduced by Estrada and Pogliani in 2008. These are positive integers $E(n)$ defined as the product of $n$ and the sum of the digits of $n$. Estrada and Pogliani suspected that there may be infinitely ...
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The orders of subgroup products and coset products
(University of Isfahan, 2025-12-01)A sect is a subset of a group given by the product of a finite number of subgroups. It is generally not a direct product nor even a subgroup of the group. For finite groups, the orders of sects are their basic invariants. ...
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Star-critical connected Ramsey numbers for 2-colorings of complete graphs
(University of Isfahan, 2025-12-01)This paper builds upon Sumner's work by further investigating the concept of connected Ramsey numbers, specifically focusing on star-critical connected Ramsey numbers. We obtain star-critical connected Ramsey numbers for ...
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On relationship between reformulated Sombor and other vertex--degree indices
(University of Isfahan, 2025-09-01)Let $G=(V,E)$, $V=\{v_1, v_2,\ldots,v_n\}$, $E=\{e_1, e_2,\ldots,e_m\}$, be a simple connected graph with $n\ge 2$ vertices and $m$ edges, with vertex degree sequence $\Delta=d_1\ge d_2\ge \cdots \ge d_n=\delta$, $ ...
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Induced Geodetic Sequence of a Graph
(University of Isfahan, 2025-09-01)A vertex subset $S$ of a graph $G=(V,E)$ is said to be a geodetic set if every vertex in $G$ is in some $u-v$ geodesic for any $u,v \in S$. The minimum cardinality of such a set is the geodetic number, which is denoted as ...
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Some results on $\lambda$-design conjecture
(University of Isfahan, 2025-09-01)Let $v$ and $\lambda$ be integers with $0\lambda$, and not all $k_j$ are equal.The ...
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Minimal graphs with respect to the multiplicative version of some vertex-degree-based topological indices
(University of Isfahan, 2025-09-01)As a real-valued function, a graphical parameter is defined on the class of finite simple graphs, and remains invariant under graph isomorphism. In mathematical chemistry, vertex-degree-based topological indices are the ...
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Density-Based clustering in mapReduce with guarantees on parallel time, space, and solution quality
(University of Isfahan, 2025-09-01)A well-known clustering problem called Density-Based Spatial Clustering of Applications with Noise~(DBSCAN) involves computing the solutions of at least one disk range query per input point, computing the connected components ...
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On the indices of certain graph products
(University of Isfahan, 2025-06-01)Molecular descriptors are numerical graph invariants that are used to study the chemical structure of molecules. In this paper, we determine the upper bound of the Sombor index based on four operations involving the ...
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Forbidden subgraphs of Co-prime graphs of finite groups
(University of Isfahan, 2025-06-01)For a finite group $G$ the co-prime graph $\Gamma(G)$ is defined as a graph with vertex set $G$ in which two distinct vertices $x$ and $y$ are adjacent if and only if $gcd(o(x),o(y))=1$ where $o(x)$ and $o(y)$ denote the ...
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Some properties of the generalized sierpiński gasket graphs
(University of Isfahan, 2025-06-01)The generalized Sierpiński gasket graphs $S[G,t]$ are introduced as the graphs obtained from the Sierpiński graphs $S(G,t)$ by contracting single edges between copies of previous phases. The family $S[G,t]$ is a ...
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A remark on sequentially Cohen-Macaulay monomial ideals
(University of Isfahan, 2025-06-01)Let $R=K[x_1,\ldots,x_n]$ be the polynomial ring in $n$ variables over a field $K$. We show that if $G$ is a connected graph with a basic $5$-cycle $C$, then $G$ is a sequentially Cohen-Macaulay graph if and only if there ...
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Commutative rings introduce a class of identifiable graphs
(University of Isfahan, 2025-06-01)Let $R$ be a commutative ring with identity, and $ \mathrm{A}(R) $ be the set of ideals with non-zero annihilator. The annihilating-ideal graph of $ R $ is defined as the graph $AG(R)$ with the vertex set $ \mathrm{A}(R) ...
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On the inverse mostar index problem for molecular graphs
(University of Isfahan, 2025-03-01)Mostar indices are recently proposed distance-based graph invariants, that already have been much investigated and found applications. In this paper, we investigate the inverse problem for Mostar indices of unicyclic and ...
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On metric dimension of edge comb product of vertex-transitive graphs
(University of Isfahan, 2025-03-01)Suppose finite graph $G$ is simple, undirected and connected. If $W$ is an ordered set of the vertices such that $|W| = k$, the representation of a vertex $v$ is an ordered $k$-tuple consisting distances of vertex $v$ with ...
