Graph theory terms

இது ஒரு மேலை நாட்டுத் தமிழறிஞரோடு ஏற்பட்ட உரையாடல். அவர் கணிதவியலாருங் கூட. அவர் graph theory தொடர்பான சில சொற்களுக்குத் தமிழாக்கம் கேட்டிருந்தார். எல்லாவற்றையும் தமிழில் இப்போது மொழிபெயர்க்காமல், மடலை அப்படியே வெளியிடுகிறேன். நம்மூர் நண்பர்களும் அறியட்டும் என்று வெளியிடுகிறேன்.

--------------------------------

You are giving me more work. :-) But I want to help. 

Many words like graph, monograph, autograph, photograph, telegraph, graphite, carve, scratch, scribe, scribble, script, ascribe, inscription, conscription, describe, transcribe, share and shear are all related. In all of these, the greek word "graphein" is staying underneath. It originally meant scratch or carve. 

This word was applied to early methods of writing, by scratching on clay tablets with a style.(see Sumerian and Indus civilizations) A similar method prevailed in Tamilnadu too. We scratch on stone-faces, wood surfaces, palm leaves, screw-pine (தாழை, Pandanus fascicularis) leaves, birch barks (burja pathra), papyri, parchments, leather skins, conch shells, mural paintings, potteries, metal surfaces (including copper plates, silver sheets and gold articles), cloths and cellulose papers. Writing refers to the use of different kinds of styli, brushes with natural dyes, chalks, charcoal/lead pencils and pens/inks on suitable surfaces. 

But too long, popular Tamil writing has limited itself to drawing, writing and the like and somehow carving has ceased to be of use in the modern times. Hence, கிறுவுதல், கிறுக்குதல், கிழித்தல், கீழ்தல், கீளுதல், கீறுதல், கீற்றுதல், கீச்சுதல் and குழித்தல் are not much used. I have been using கிறுவுதல் for quite some time around 25 years. I would suggest to use கிறுவு or கிறுவம் (larger கிறுவு) for graph.

Theory is தேற்று. Theorem = தேற்றம், since தேறுதல் = தெளிதல் and தேற்று = தெளிந்த கூற்று. Then graph theory would become கிறுவத் தேற்று. path is பாதை 

cycle is சுரி. acyclic = சுரியா. Direction is related to turning. திரும்புதல், The intransitive verb is திரும்பு and திருகு.  The transitive verb is திருக்கு. This can also become a noun in folk usage. திருக்கு. becomes திக்கு on further use. This would eventually morph into திசை. The linguistic term "directed acyclic graph" would become "திருக்கிய சுரியாக் கிறுவம்" in Tamil.

Every vertex is caused by turns. turning is curving. வளைதல். முனங்குதல்>முணங்குதல் is also turning. முணங்கு is end. அந்தத் தெரு முணங்கில் இருக்கும் வீடு = house in the street end. In school mathematics, vertex is referred to as முனை. But there is also an old word called வட்கு. This is included in Pingalam nigandu. Even today we use through colloquial speech in Sivagangai Distict as வக்கு. The term "வக்கு இல்லாதவன்" means one who does not have any ends to sustain. So both முனை and வட்கு can be used for vertex.

For connection/connect, Atlanta Periannan Chandrasekaran had suggested almost 17/18 years back, கணுக்குதல். This brings out the noun கணு (node) in sugar cane (கரும்பு). Every node is connection. Since then I have been using that. It has not given me any problem.

Components are elements that are put together. There are host of words related to this. compose, composite, compost, compute, compound, positive etc. I can write a separate essay on the concept behind these words. பொதிதல் and புணைதல் are related to this word. The prefix "com" is normally left out in Tamil. (it is understood to be there from behind. So புணை would ne ideal for component. So connected components is கணுக்கிய புணைகள். On consolidation, the terms you have asked for are:

graph = கிறுவு, கிறுவம்

graph theory = கிறுவத் தேற்றம்

path = பாதை 

cycle = சுரி

directed acyclic graph = திருக்கிய சுரியாக் கிறுவம்

vertex = முனை, வட்கு

connected components = கணுக்கிய புணைகள்.

இராம. கி