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; ...

Abstract The objective of clustering is to discover natural groups in datasets and identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics data. problem can be seen as detecting inherent separations between a given point set metric space governed by similarity function. pairwise similarities all data objects form weighted graph whose...

Recently, Tittmann et al. introduced the subgraph component polynomial and showed that its power for distinguishing graphs is quite different from the power of other graph polynomials that appear in the literature such as the matching polynomial, the Tutte polynomial, the characteristic polynomial, the chromatic polynomial, etc. The subgraph component polynomial enumerates vertex induced subgra...