# Algebraic Graph Theory by N. Biggs

By N. Biggs

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**Extra resources for Algebraic Graph Theory**

**Example text**

19, 'Some individual is identical to itself'. So far all the graphs we have used involving lines of identity have been such that the lines were either entirely enclosed in QD

4 with Fig. 2. Fig. 2 means 'If Q is true then R is true'. ) is true'. By analogy, therefore, Fig. 4 must mean: 'It is false that Q is true and is true'. But·O is the pseudograph, and has (always) the value false, or 2; hence the value of the fllSt area of Fig. 4 is 2, and the value of the entire graph is 1, or true. Fig. 4 then, is true regardless of the value of Q, and regardless of the value of Fig. 2; and it follows from this (trivially) that the inference of Fig. 4 from Fig. 2 by means of Rl is a valid.

7 Figs. 6 and 7 are equivalent according to C9. Fig. 4 means 'Whatever is F is also G'. By Rl it can be transfonned into Figs. 8 and 9~ which mean 'If something is F then something is G'. That Figs. 8 and 9 are equivalent follows from the endoporeutic method of interpretation, according to which it is the outennost extremity of a line of identity that detennines how it is to be read. Fig. 8 Fig. 9 R2. The rule of insertion. (or portions of lines) oddly enclosed on the same area, may be joined, R2 justifies the transfonnation of Fig.