Talk:Graph operations

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Added "complete join" as an alternative name for "graph join". "Complete join" is used in the literature and on this WIKI. I added a redirect and changed the use on the page Extremal graph theory to a link. Leen Droogendijk (talk) —Preceding undated comment added 04:49, 21 September 2013 (UTC)Reply

This defines a simple way of constructing a larger graph from a graph and an integer:

We construct graph H from graph G and integer N, by replacing each vertex of G by N copies of itself. Two vertices of H are connected iff their originals in G are connected.

We can regard this as the "lexicographical product" of G and the edgeless graph with N vertices. But that seems unnecessarily complicated for a relatively simple construction.

Is this construction actually handled in the article somewhere? If not, should it be?, and what is it called?

Maproom (talk) 08:39, 19 December 2013 (UTC)Reply

The operation you are describing is called the multiple of a graph. I read that in a graph theory paper, but I cannot now find it, since the terms multiple and graph are associated with too many other things. 173.242.174.245 (talk) 18:57, 5 November 2024 (UTC)Reply

An example of this terminology is in L. Lovasz's paper "A characterization of perfect graphs", from 1972. 128.172.33.44 (talk) 16:49, 6 August 2025 (UTC)Reply

A new operation on complete graph is known as Avi's Operation. Let say we have a complete graph K(n) Now we want to partition the complete graph into sub complete graph smaller than earlier one such the sum of edges of both sub complete graph is equal to edge of earlier complete graph k(n) For example Let say k(4) , here is 4 vertex so there is 6 edges now we want to partition the Graoh into two sub complete graph and that is k(3) So 6=3+3 Here 3 and 6 ate number of edges But we can't portioned k(5) into two sub complete graph because There is no any such complete graph such that the sum of their edges is equal to edge of k(5). — Preceding unsigned comment added by 123Avinsh M3001 (talk • contribs) 03:05, 17 January 2019 (UTC)Reply

How can you partition a K₄ into two K₃s? Maproom (talk) 08:18, 17 January 2019 (UTC)Reply

You cant do that because there are only some special complete graph which can be partioned into two others comolete graph 123Avinsh M3001 (talk) 13:42, 9 July 2019 (UTC)Reply

You cant do that because there are only some special complete graph which can be partioned into two others comolete graph 123Avinsh M3001 (talk) 13:42, 9 July 2019 (UTC)Reply