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What is correct:

"In 1960 Harary formulated the cell growth problem as a problem of graph enumeration"

or

"In 1960 Harary formulated the cell growth problem as a graph enumeration problem"?

Thanks,

Alex.

"In 1960 Harary formulated the cell growth problem as a problem of graph enumeration"

or

"In 1960 Harary formulated the cell growth problem as a graph enumeration problem"?

Thanks,

Alex.

1 2

google does not give very representative numbers (1 vs. 9).

What is correct: "In 1960 Harary formulated the cell growth problem as a problem of graph enumeration" or "In 1960 Harary formulated the cell growth problem as a graph enumeration problem"?

I don't think I would use either, but perhaps I'm misunderstanding. What is the purpose of the graph? Is it actually to solve some aspect of a problem, or is it to illustrate a statistic more clearly? In other words, having created and consulted the graph, do you have new information, or just a better understanding of the data?

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What is correct: "In 1960 Harary formulated the cell growth ... formulated the cell growth problem as a graph enumeration problem"?

I don't think I would use either, but perhaps I'm misunderstanding. What is the purpose of the graph? Is it ... words, having created and consulted the graph, do you have new information, or just a better understanding of the data?

In general mathematics, both. In the specific situation, a graph is simply some geometric figure consisting of n nodes (=vertices=sites), which are somehow connected by line segments (edges). An example is the metro plan where nodes are the stations and line segments are the tubes between the stations.

If we draw graphs on a sheet of paper, the edges may be allowed to overlap. Typical questions are

"How many different graphs are there with n nodes" or "How many graphs are there with m edges so that each node is connected to at least 3 other nodes directly". The most general question is "How many graphs are there with property X". This is the question Harary posed where "X" was some suitable property which is a bit complicated to explain it here.

I don't think I would use either, but perhaps I'm ... new information, or just a better understanding of the data?

In general mathematics, both. In the specific situation, a graph is simply some geometric figure consisting of n nodes (=vertices=sites), which are somehow connected by line segments (edges).

The sentences you proposed imply that there is some problem, and that in order to solve the problem Harary resorted to graphs. Is this the case? If so write:

"In 1960 Harary formulated the cell growth problem in graphic format in an effort to solve it."

Otherwise write:

"In 1960 Harary formulated cell growth in a graphic format."

What is correct: "In 1960 Harary formulated the cell growth problem as a problem of graph enumeration" or "In 1960 Harary formulated the cell growth problem as a graph enumeration problem"?

Both are possible. The feel is different though.

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What is correct: "In 1960 Harary formulated the cell growth problem as a problem of graph enumeration" or "In 1960 Harary formulated the cell growth problem as a graph enumeration problem"?

Either looks fine to me. Mike Hardy

What is correct: "In 1960 Harary formulated the cell growth ... formulated the cell growth problem as a graph enumeration problem"?

I don't think I would use either, but perhaps I'm misunderstanding. What is the purpose of the graph? Is it ... words, having created and consulted the graph, do you have new information, or just a better understanding of the data?

You miss the point completely. Harary is a well-known mathematician who, as everyone (except non-mathematicians) knows, worked on the kind of COMBINATORIAL problems that are called graph enumeration problems. In other words, the "graphs" he was working with were not the kinds of things they tell you to call "graphs" in high school, whose purpose is a illustrate statistical data, etc. Mike Hardy

"In 1960 Harary formulated the cell growth problem in graphic format in an effort to solve it." Otherwise write: "In 1960 Harary formulated cell growth in a graphic format."

NO, NO, NO, NO, NO!! Harary did nothing of the sort. The "graphs" he was enumerating were not "graphic" at all, in the sense you think of in 8th grade when they talk about graphs.

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