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Results tagged with graph-theory
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user 11856
Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
33
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What does this connection between Chebyshev, Ramanujan, Ihara and Riemann mean?
It all started with Chris' answer saying returning paths on cubic graphs without backtracking can be expressed by the following recursion relation:
$$p_{r+1}(a) = ap_r(a)-2p_{r-1}(a)$$
$a$ is an …
- 457
3
votes
0
answers
461
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How does the topology of the graphs' Riemann surface relate to its knot representation?
Let's consider the following bipartite cubic planar non-simple graph
$\hskip2.3in$
Looking at the orientation of the edges around the vertices, it is obvious that left and right are oriented opposite. …
- 457
2
votes
1
answer
221
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Mapping $\Delta(2,2,2)\mapsto \Delta(4,4,2)$
Looking at the images below, you recognize that the adjacency matrix of the graph $A_G$ splits up into three different colored submatrices, with $A_G=A_r+A_b+A_d$ (where $d$ is dark, damn...).
It's o …
- 457
1
vote
learning sources about Ihara Coefficient
I can recommend this paper: The coefficients of the Ihara zeta function
by Geoffrey Scott and Christopher Storm
- 457
1
vote
0
answers
74
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3-edge colorings for special cubic graphs on a double torus
In Complexity of 3-edge-coloring in the class of cubic graphs with a polyhedral embedding in an orientable surface it is proven that the task to find these colorings is NP-complete in the general case …
- 457