How Do You Spell HAMILTONIAN CYCLE?

Pronunciation: [hˌamɪltˈə͡ʊni͡ən sˈa͡ɪkə͡l] (IPA)

The Hamiltonian cycle is a term in graph theory and in mathematics. Its spelling may seem tricky, but using the IPA phonetic transcription can help. The word is pronounced /hæmɪlˈtoʊniən/ - "ham-uh l-tow-nee-uhn". The stress is on the second syllable, and each sound in the word can be broken down by the IPA symbols. The "h" is pronounced as in "hat," followed by "æ" as in "cat." The "m" and "l" sounds lead into a long "o" sound represented by "ow." The final syllable is pronounced "nee-uhn".

HAMILTONIAN CYCLE Meaning and Definition

1. A Hamiltonian cycle refers to a term used in discrete mathematics and graph theory to describe a closed loop or cycle that visits every vertex of a given undirected graph exactly once. Specifically, a Hamiltonian cycle in a graph refers to a path that starts and ends at the same vertex, with each vertex being visited only once. It is named after the Irish mathematician Sir William Rowan Hamilton, who first introduced the concept in the 19th century.

   In order for a graph to possess a Hamiltonian cycle, it must satisfy certain conditions. Firstly, all vertices in the graph must be connected to one another, meaning that there should be an edge connecting every pair of vertices. Additionally, it is essential for the Hamiltonian cycle to be able to traverse through every vertex, without skipping any.

   The Hamiltonian cycle is a fundamental concept in graph theory and serves as a tool to analyze and understand various aspects of graph structures. It has numerous applications in areas such as computer science, transportation planning, communication networks, and manufacturing systems. Determining the existence of a Hamiltonian cycle in a graph is challenging, as it is considered an NP-complete problem in computational complexity theory, which implies that no efficient algorithm exists to solve it for large graphs.

Common Misspellings for HAMILTONIAN CYCLE

• gamiltonian cycle
• bamiltonian cycle
• namiltonian cycle
• jamiltonian cycle
• uamiltonian cycle
• yamiltonian cycle
• hzmiltonian cycle
• hsmiltonian cycle
• hwmiltonian cycle
• hqmiltonian cycle
• haniltonian cycle
• hakiltonian cycle
• hajiltonian cycle
• hamultonian cycle
• hamjltonian cycle
• hamkltonian cycle
• hamoltonian cycle
• ham9ltonian cycle
• ham8ltonian cycle
• hamiktonian cycle

Etymology of HAMILTONIAN CYCLE

The word "Hamiltonian cycle" is derived from the name of the Irish mathematician William Rowan Hamilton, who first introduced the concept in the 19th century. Hamilton made significant contributions to the field of graph theory, particularly in the study of paths and circuits in graphs. The term "Hamiltonian cycle" was coined to honor his pioneering work in this area.

Plural form of HAMILTONIAN CYCLE is HAMILTONIAN CYCLES