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Main Authors:	Dilaver, Gökçen, Altinok, Selma
Format:	Preprint
Published:	2025
Subjects:	Combinatorics 05C25, 05C78, 05E16, 05C60
Online Access:	https://arxiv.org/abs/2512.00429
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Group irregularity strength of disconnected graphs
by: Cichacz, Sylwia, et al.
Published: (2023)

Isomorphism of Clean Graphs over $\mathbb{Z}_n$ and Structural Insight into $M_2(\mathbb{Z}_p)$
by: Djuang, Felicia Servina, et al.
Published: (2025)

Graph Cordiality -- Extremes and Preservers
by: Beasley, LeRoy b.
Published: (2024)

Spectra of Group Vertex Magic Graphs
by: Balamoorthy, S., et al.
Published: (2024)

On the Clean Graph of a Ring
by: Singh, Randhir, et al.
Published: (2024)

Distinguishability and linear independence for $H$-chromatic symmetric functions
by: Lin, Shao Yuan, et al.
Published: (2025)

Homotopy Covers of Graphs
by: Chih, Tien, et al.
Published: (2020)

Splines on Cayley Graphs of the Symmetric Group
by: Lesnevich, Nathan R. T.
Published: (2024)

On zero-divisor graph of the ring of Gaussian integers modulo $2^n$
by: Venkatesan, Aruna, et al.
Published: (2025)

Forbidden Subgraphs of Prime Order Element Graph
by: Manna, Tapa, et al.
Published: (2024)

On distance magic circulants of valency 6
by: Miklavič, Štefko, et al.
Published: (2022)

A unified Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups
by: Gollin, J. Pascal, et al.
Published: (2022)

A unified half-integral Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups
by: Gollin, J. Pascal, et al.
Published: (2021)

Descent sets of cyclic permutations in types B and D
by: Liu, Kevin
Published: (2025)

Descents and flag major index on conjugacy classes of colored permutation groups without short cycles
by: Liu, Kevin, et al.
Published: (2025)

Equivariant log-concavity of graph matchings
by: Li, Shiyue
Published: (2022)

Fundamental Groups of Hamming Graphs
by: Behal, Keira, et al.
Published: (2023)

Chromatic quasisymmetric functions of the path graph
by: Aliniaeifard, Farid, et al.
Published: (2024)

Spectral Bounds of the Generating Graph of $\mathbb{Z}_n.$
by: Samant, Kavita, et al.
Published: (2025)

Finding automorphism groups of double coset graphs and Cayley graphs are equivalent
by: Barber, Rachel, et al.
Published: (2024)

Monodromy representation of graphs
by: Yuan, Kai, et al.
Published: (2025)

Recognizing bicoset digraphs which are $X$-joins and automorphism groups of bicoset digraphs
by: Barber, Rachel, et al.
Published: (2024)

Zero-sum partitions of Abelian groups and their applications to magic- and antimagic-type labelings
by: Cichacz, Sylwia, et al.
Published: (2022)

Bizonotopal Graphical Algebras
by: Kirillov, Anatol, et al.
Published: (2024)

D-Antimagic Labelings of Oriented Star Forests
by: Abrar, Ahmad Muchlas, et al.
Published: (2025)

Chromatic numbers with open and nonzero local modular constraints
by: Herden, Daniel, et al.
Published: (2025)

Chromatic numbers with closed local modular constraints
by: Herden, Daniel, et al.
Published: (2025)

A Study on Type-2 Isomorphic Circulant Graphs: Part 8: $C_{432}(R)$, $C_{6750}(S)$ -- each has 2 types of Type-2 isomorphic circulant graphs
by: Kamalappan, Vilfred
Published: (2026)

Counterexample to Babai's lonely colour conjecture
by: Davies, James, et al.
Published: (2024)

On the BCI Problem
by: Dobson, Ted, et al.
Published: (2024)

Clean Graphs and Idempotent Graphs over Finite Rings: An Approach Based on Z_n
by: Djuang, Felicia Servina, et al.
Published: (2025)

To see the forest for the trees: On the infinite divisibility of unlabeled forests
by: Bassan, Michal, et al.
Published: (2025)

The Chromatic Symmetric Function for Unicyclic Graphs
by: Bingham, Aram, et al.
Published: (2025)

Chromatic symmetric functions and polynomial invariants of trees
by: Aliste-Prieto, José, et al.
Published: (2024)

A study on Type-2 isomorphic circulant graphs. Part 2: Type-2 isomorphic circulant graphs of orders 16, 24, 27
by: Kamalappan, Vilfred
Published: (2025)

A study on Type-2 isomorphic circulant graphs. Part 4: 960 triples of Type-2 isomorphic circulant graphs $C_{54}(R)$
by: Kamalappan, Vilfred
Published: (2026)

A study on Type-2 isomorphic circulant graphs. Part 3: 384 pairs of Type-2 isomorphic circulant graphs $C_{32}(R)$
by: Kamalappan, Vilfred
Published: (2026)

A study on Type-2 isomorphic circulant graphs. Part 5: Type-2 isomorphic circulant graphs of orders 48, 81, 96
by: Kamalappan, Vilfred
Published: (2026)

A study on Type-2 isomorphic circulant graphs. Part 10: Type-2 isomorphic $C_{np^3}(R)$ w.r.t. $m$ = $p$ and related groups
by: Kamalappan, Vilfred, et al.
Published: (2022)

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// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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