The k-dimensional Weisfeiler-Leman algorithm (k-WL) is a very useful combinatorial tool in graph isomorphism testing. We address the applicability of k-WL to recognition properties. Let G be an input with n vertices. show that, if prime, then vertex-transitivity can seen straightforward way from output 2-WL on and vertex-individualized copies G. This perhaps first non-trivial example using for ...

In Section 4.5, “Assertion 4-2 based on Theorem 1, 2, 3, 4: Two undirected and simple graphs G1 G2. The number of nodes for the two is same as n. edges m. There are no isolated in both graphs. vertex edge adjacency matrices generated V1 V2, E1 E2. sums rows/columns produce four sets an array aV1, bV2, aE1, bE1 If only if ∑n k=1 ak = bk (ak V1)2 (bk V2)2, then aV1 bV2 a permutation another set; ...

The Tisserand graph (TG) is a graphical tool commonly employed in the preliminary design of gravity-assisted trajectories. TG two-dimensional map showing essential orbital information regarding Keplerian orbits resulting from close passage by one or more massive bodies, given magnitude hyperbolic excess speed ($v_{\infty}$) and minimum allowed pericenter height for each passage. Contours consta...