Results 31 to 40 of about 848 (243)

GRACEFUL CHROMATIC NUMBER OF SOME CARTESIAN PRODUCT GRAPHS

Ural Mathematical Journal, 2023
A graph \(G(V,E)\) is a system consisting of a finite non empty set of vertices \(V(G)\) and a set of edges \(E(G)\). A  (proper) vertex colouring of \(G\) is a function \(f:V(G)\rightarrow \{1,2,\ldots,k\},\) for some positive integer \(k\) such that ...
I Nengah Suparta, Mathiyazhagan Venkatachalam, I Gede Aris Gunadi, Putu Andi Cipta Pratama   +3 more
doaj   +1 more source

Strongly graceful graphs

Discrete Mathematics, 1980
AbstractIn this paper, we prove that the n-cube is graceful, thus answering a conjecture of J.-C. Bermond and Gangopadhyay and Rao Hebbare. To do that, we introduce a special kind of graceful numbering, particular case of α-valuation, called strongly graceful and we prove that if a graph G is strongly graceful, G + K2 is also strongly graceful.
openaire   +3 more sources

Graceful And Graceful Labeling Of Graphs

, 2018
{"references": ["1.\tJ. A. Gallian, A Dynamic survey of graph labeling, The electronic journal of combinatory 16 (2009).DS6. 2.\tI. Gutman, The energy of a graph, Ber. Math-satist. sekt. Forschungsz. Graz 103 (1978), 1-22. 3.\tGutman and B. Zhou, Laplacian energy of a graph, linear algebra appl. 414 (2006), 29-37. 4.\tI.
M. Soundharya, R. Balakumar
openaire   +2 more sources

A New Measure for Gracefulness of Graphs

Electronic Notes in Discrete Mathematics, 2015
Abstract Let G = ( V , E ) be a ( p , q ) -graph without isolated vertices. The gracefulness grac ( G ) of G is the smallest positive integer k for which there exists an injective function f : V → { 0 , 1 , 2 , … , k } such that the edge induced function g f : E → { 1 , 2 ...
Jessica Pereira, Tarkeshwar Singh, S. Arumugam 0001   +2 more
openaire   +2 more sources

Adaptive Foam 3D Printing of Ultralight and Multifunctional Materials

Advanced Engineering Materials, EarlyView.
Adaptive foam 3D printing, enabled by expandable microspheres, imparts cellular structures to thermoplastic and thermosetting polymers, manufactured through a variety of processes including fused filament fabrication, direct ink writing, digital light processing, and inkjet printing.
Nariman Rajabifar, Amir Ameli
wiley   +1 more source

Guanosine‐Quadruplex Hydrogels as Dynamic, Mechanically Tunable and Ion Conductive 3D Scaffolds for Cell Culture Applications

Advanced Functional Materials, EarlyView.
Versatile guanosine‐quadruplex (GQ) hydrogels are developed as dynamic biomatrices for cell culture. These scaffolds are fabricated under mild aqueous conditions, present improved stability, tunable mechanical properties within physiological ranges; fibrillar, porous microstructure, ion conductivity, and cytocompatibility.
Neha Thakur, Minye Jin, Pavel Milkin, Deepa Negi, Carla Cofiño Fabres, Hubert Gojzewski, Leonid Ionov, Alla Synytska, Andries van der Meer, Robert Passier, Julieta I. Paez   +10 more
wiley   +1 more source

Intelligent Sky Guardians (InSkyGuard): An Aerial Robotic Swarm for Autonomous Detection and Entrapment of Rogue Multirotors

Advanced Robotics Research, EarlyView.
Intelligent Sky Guardians (InSkyGuard) is introduced as a four‐drone swarm that autonomously detects, tracks, and safely captures rogue drones using a coordinated net system. Computer vision and leader–follower control architecture enable synchronized enclosure, while integrated failsafes enhance system reliability. Validated through closed‐environment
Joshua Hastings, Levanya Dewanarayana, Iline Shaju, Haider Al‐Wizni, Sampson Marquis, Weicheng Huang, Pooya Sareh   +6 more
wiley   +1 more source

Learning‐Based Soft Robotic Grasping: Recent Progress and Remaining Challenges

Advanced Robotics Research, EarlyView.
This review analyzes learning‐based soft robotic grasping from a pipeline‐oriented perspective, encompassing soft gripper design, multimodal sensing, and learning‐based planning and control. It surveys key neural network architectures and benchmark datasets and identifies critical challenges such as sim‐to‐real transfer, generalization, and continual ...
Arnab Majumder, Jelizaveta Konstantinova, Graham Deacon, Kaspar Althoefer   +3 more
wiley   +1 more source

An Investigation on the Edge-gracefulness of Bubble Sort, Bubble Sort Star, and Kulli-Cycle Windmill Graphs

Science and Technology Indonesia
A fundamental area of graph theory, graph labeling concerns the assignment of integers to the vertices, edges, or both of a graph under specified constraints. One of the many types of graph labeling is edge-graceful labeling.
John Rafael M. Antalan, Richard Tagle, Aaron Angel, John Loureynz F. Gamurot   +3 more
doaj   +1 more source

Graceful numbers

International Journal of Mathematics and Mathematical Sciences, 2002
We construct a labeled graph D(n) that reflects the structure of divisors of a given natural number n. We define the concept of graceful numbers in terms of this associated graph and find the general form of such a number.
Kiran R. Bhutani, Alexander B. Levin
doaj   +1 more source