rushil
- 40
- 0
Everyone probably know the famous problem consisting of a circuit having 12 resistors in the shape of a cube such that the resistors make up the edges. We pass current from one vertex and are required to find the effective resistance between this vertex and another one (the difficulty of the problem depends upon which vertexes are considered!)
In Physics, we usually solve this problem by assuming some symmetry considerations like equal partition of current or equal voltages etc. While studying Graph Theory in Alan Tucker's book, I cam across a similar example where he asked whether 2 graphs, one like the cubical circuit above and another circular graph were isomorphic. While his question ended in a negative there, I thought, could it be possible to solve the problem without any assumptions by finding a suitable, simple isomorphic graph that can be easily solved! Before getting down to some brainstorming, I just want to know, has anyone of you (or somebody you know) considered this problem before. Are you aware of a solution to the above problem? Please post what you think and your possible solutions!
In Physics, we usually solve this problem by assuming some symmetry considerations like equal partition of current or equal voltages etc. While studying Graph Theory in Alan Tucker's book, I cam across a similar example where he asked whether 2 graphs, one like the cubical circuit above and another circular graph were isomorphic. While his question ended in a negative there, I thought, could it be possible to solve the problem without any assumptions by finding a suitable, simple isomorphic graph that can be easily solved! Before getting down to some brainstorming, I just want to know, has anyone of you (or somebody you know) considered this problem before. Are you aware of a solution to the above problem? Please post what you think and your possible solutions!