graph theory - Is there a purely set-theoretic expression of the Euler characteristic?

Graph idea from a class idea perspective retort

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Graph idea from a class idea perspective

Are there any textbooks on graph idea written for a class theorist?

It would in all probability maintain to breathe on directed graph idea, but when there’s some trick we will make use of to speak about undirected graphs as properly that might breathe fascinating.

A tiny extra particularly, I’m on the lookout for a textual content that begins by defining directed graphs and paths, then defines the patent class out of a given directed graph with paths as arrows, then proceeds to gather outcomes about directed graphs utilizing this class.

Most connections I graze made between class idea and graph idea are within the different path, taking the underlying graph of a class and maxim one thing concerning the graph to gather a end result concerning the class, however as somebody cozy with classes and never cozy with graphs this strategy is not significantly illuminating for me.

Further, except I’m mistaken, these constructions quantity to an equivalence (possibly airplane an isomorphism?) between the class of directed graphs and the class of classes, so it feels affection we should always breathe in a position to say one thing about directed graphs from this attitude.

Any references are appreciated.

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