chapter: graph theory Paul Erdos (1913-1996) was one of the most prolific mathem
ID: 3006085 • Letter: C
Question
chapter: graph theory
Paul Erdos (1913-1996) was one of the most prolific mathematicians of all time. He was the author or co-author of nearly 1500 papers. Mathematicians who co-authored a paper with Erd6s are said to have Erdos number one. Mathematicians who did not co-author a paper with Erd6s but who co-authored a paper with a mathematician whose Erd6s number is one are said to have Erdos number two. Higher Erdos numbers are defined similarly. For example, the author of this book has Erdos number five. Johnsonbaugh co-authored a paper with Tadao Murata, Murata co-authored a paper with A. T. Amin, Amin co-authored a paper with Peter J. Slater, Slater co-authored a paper with Frank Harary, and Harary co-authored a paper with Erdos. Develop a graph model for ErdSs numbers. In your model, what is an Erd6s number?Explanation / Answer
The vertices are mathematicians, and an edge connects two mathematicians if they co–authored a paper.
The Erdos number of a mathematician m is the length of a shortest path from m to Erdos.
v0 = Erdos
v1 = Harary
v2 = Slater
v3 = Amin
v4 = Murata
v5 = Johnsonbaugh
e1 = ( v0, v1 ) = ( Erdos, Harary )
e2 = ( v1, v2 ) = ( Harary, Slater )
e3 = ( v2, v3 ) = ( Slater, Amin )
e4 = ( v3, v4 ) = ( Amin, Murata )
e5 = ( v4, v5 ) = ( Murata, Johnsonba
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