Let G be a graph with a nonempty edge set, we denote the rank of the adjacency matrix of G and the term rank of G, by rk ( G ) and Rk ( G ) , respectively. It was conjectured [C. van Nuffelen, Amer. Math. Monthl
A.A. RazborovA. Razborov. The gap between the chromatic number of a graph and the rank of its adjacency matrix is superlinear. Discrete Mathematics, 108(1-3):393-396, 1992.The gap between the chromatic number of a graph and the rank of its adjacency matrix is superlinear, Discrete ...
Rank of graphs Matching number Chromatic index Independence number 1. Introduction Throughout this paper we consider simple graphs. The adjacency matrix A(G) of a graph G with vertex set V(G)={xi:1≤i≤v} is defined to be an v×v symmetric matrix [aij] such that aij=1 if xi is ad...
et al. The physics of higher-order interactions in complex systems. Nat. Phys. 17, 1093 (2021). Article CAS Google Scholar Wilf, H. S. The eigenvalues of a graph and its chromatic number. J. Lond. Math. Soc. 1, 330 (1967). Article MathSciNet Google Scholar Donath, W. E. &...
In the end, the Schein rank of a fuzzy matrix has been considered by the view of general decomposition. For a given fuzzy matrix, it is proved that its Schein rank is equal to the chromatic number of a simple graph generated by it. Thus, calculating the Schein rank of a fuzzy matrix ...
We show that, for any 2-connected graph $G e K_{3,3}$ on at least 6 nodes, $egd(G)le 2$ if and only if $sla(G)le 2$. 阅读PDF 1 被引用 · 0 笔记 引用 Spectral bounds for the independence ratio and the chromatic number of an operator Christine BachocFernando Mário de ...
We show that a connected graph with real flow number p / q +1, where p and q are two relatively prime numbers must have cycle rank at least p + q - 1. A special case of this result yields that the real flow number of a 2-connected cubic graph with chromatic index 4 and order ...
Lovász and Saks [12] observed (see also [13]) that this problem is closely related to bounding the chromatic number of graphs, whose adjacency matrix has bounded rank. Indeed, ifc(r) denotes the maximum of\text{ CC}^{det}(f)among everyfof rankr, then\chi (G)\le 2^{c(r+1)}for...
The mammary glands of age-matched females with concomitant ablation of Rank appeared largely nor- mal, displaying a significantly lower number of MINs and no detectable carcinomas (Figure 1A-1C and Sup- plementary information, Figure S3). Quantification of branching points in whole mount staining...
C. Van Nuffelen, “Rank, clique and chromatic number of a graph,” Lect. Notes Inf. Sci., 38 , 605–611 (1982).C. Van Nuffelen. Rank, clique and chromatic number of a graph. In System modeling and optimization (New York, 1981), volume 38 of Lecture Notes in Control and Inform....