Results 31 to 40 of about 96 (83)

On Grundy Total Domination Number in Product Graphs

Discussiones Mathematicae Graph Theory, 2021
A longest sequence (v1, . . ., vk) of vertices of a graph G is a Grundy total dominating sequence of G if for all i, N(υj)\∪j=1i-1N(υj)≠∅N({\upsilon _j})\backslash \bigcup\nolimits_{j = 1}^{i - 1} {N({\upsilon _j})} \ne \emptyset .
Brešar Boštjan, Bujtás Csilla, Gologranc Tanja, Klavžar Sandi, Košmrlj Gašper, Marc Tilen, Patkós Balázs, Tuza Zsolt, vizer Máté   +8 more
doaj   +1 more source

A New Kind of Dominated Coloring of Some Special Graphs

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper introduces the concept of locating‐dominated coloring, a new graph coloring parameter that merges the properties of dominated coloring and locating coloring. For a connected graph G, a locating‐dominated coloring is defined as a proper dominated k‐coloring of G using an ordered partition of V(G) to k‐color classes Π = (C1, C2, …, Ck) such ...
F. Poryousefi, A. Erfanian, M. Nasiri, Pramita Mishra   +3 more
wiley   +1 more source

A Note on the Thue Chromatic Number of Lexicographic Products of Graphs

Discussiones Mathematicae Graph Theory, 2018
A sequence is called non-repetitive if none of its subsequences forms a repetition (a sequence r1r2⋯r2n such that ri = rn+i for all 1 ≤ i ≤ n). Let G be a graph whose vertices are coloured.
Peterin Iztok, Schreyer Jens, Škrabul’áková Erika Fecková, Taranenko Andrej   +3 more
doaj   +1 more source

On Well-Covered Direct Products

Discussiones Mathematicae Graph Theory, 2022
A graph G is well-covered if all maximal independent sets of G have the same cardinality. In 1992 Topp and Volkmann investigated the structure of well-covered graphs that have nontrivial factorizations with respect to some of the standard graph products.
Kuenzel Kirsti, Rall Douglas F.
doaj   +1 more source

Analysis of Wiener and Hyper‐Wiener Indices in Generalized R‐Vertex Corona and Join Graphs of Diameter at Most Three

Journal of Mathematics, Volume 2026, Issue 1, 2026.
Among various graph products, the corona product continues to inspire novel research. Subdivision graphs play a key role in understanding graph behaviour under edge modifications. The estimation of Wiener index under various graph operations is of considerable importance and has attracted substantial attention in chemical graph theory.
Vimal M., Md. Ashraful Alam, Kalaimurugan G., Vinnarasi L., Ammar Alsinai   +4 more
wiley   +1 more source

Construction of Albertson Cospectral and Albertson Equienergetic Graphs Using Graph Operations

Journal of Mathematics, Volume 2026, Issue 1, 2026.
The energy of a graph is an invariant calculated as the sum of the absolute eigenvalues of its adjacency matrix. This concept extends to various types of energies derived from different graph‐related matrices. This paper explores the spectral properties of Albertson energy and Albertson spectra.
Jane Shonon Cutinha, Sabitha D’Souza, Swati Nayak, G Muhiuddin   +3 more
wiley   +1 more source

(Open) packing number of some graph products [PDF]

Discrete Mathematics & Theoretical Computer Science, 2020
The packing number of a graph $G$ is the maximum number of closed neighborhoods of vertices in $G$ with pairwise empty intersections. Similarly, the open packing number of $G$ is the maximum number of open neighborhoods in $G$ with pairwise empty ...
Doost Ali Mojdeh, Iztok Peterin, Babak Samadi, Ismael G. Yero   +3 more
doaj   +1 more source

Harmonic–Arithmetic Index for the Generalized Mycielskian Graphs and Graphenes With Curvilinear Regression Models of Benzenoid Hydrocarbons

Computational and Mathematical Methods, Volume 2025, Issue 1, 2025.
The generalized Mycielskian graphs are known for their advantageous properties employed in interconnection networks in parallel computing to provide efficient and optimized network solutions. This paper focuses on investigating the bounds and computation of the harmonic–arithmetic index of the generalized Mycielskian graph of path graph, cycle graph ...
Pooja Danushri Namidass, Shobana Loganathan, Pramita Mishra   +2 more
wiley   +1 more source

Some Observations on the Smallest Adjacency Eigenvalue of a Graph

Discussiones Mathematicae Graph Theory, 2020
In this paper, we discuss various connections between the smallest eigenvalue of the adjacency matrix of a graph and its structure. There are several techniques for obtaining upper bounds on the smallest eigenvalue, and some of them are based on Rayleigh
Cioabă Sebastian M., Elzinga Randall J., Gregory David A.   +2 more
doaj   +1 more source

The Vertex-Rainbow Connection Number of Some Graph Operations

Discussiones Mathematicae Graph Theory, 2021
A path in an edge-colored (respectively vertex-colored) graph G is rainbow (respectively vertex-rainbow) if no two edges (respectively internal vertices) of the path are colored the same.
Li Hengzhe, Ma Yingbin, Li Xueliang
doaj   +1 more source