TRIANGLESSTOCHASTIC matricesBIPARTITE graphsLOGICAL predictionEDGES (Geometry)Bollobás and Nikiforov (J. Combin. Theory Ser. B.97 (2007) 859–865) conjectured the following. If G is a Kr 1-free graph on at leas
This has led to the spectral characterization of many (unsigned) graphs including the friendship graphs (consisting of a number of edge-disjoint triangles meeting in one vertex). Here we find infinite families of signed graphs with the same spectrum as a friendship graph, whilst there is only ...
Since α(G)=2, G¯ has no triangles. It is well-known that the complement of an odd cycle Cn with n≥5 has at least three positive eigenvalues. Therefore, by interlacing, G¯ has no induced odd cycle, so G¯ is bipartite and the adjacency matrix A of G has the following ...
The coefficients of the characteristic polynomial P(G;x) of a connected graph G satisfy: c1=0,−c2 is the number of edges and −c3 is twice the number of triangles of G. Let A be the adjacency matrix of a graph G. It is well known that the (i,j)-th element aij(k) of the...
sphere coneorcylinderofrevolution Alsothevertexofageneralconeorthedirectionsoftherulingsofageneralcylindercanbecomputed Inallthesecases onewillusetheseap proximantsforsegmentationofthedataand–ifnecessary–asaninitial naltshouldbeperformedbyamethodworkingdirectlyontherelevantdatapointspi seedetailsandreferencesinthe...
We examine the general dimensional relation between the shape space of the n-simplexes and the subspace of their achiral sets. It is found that the only simplexes that can be partitioned into ''left-handed'' and ''right-handed'' classes are the triangles in Euclidean 2-space....
In this paper, we first present a new upper bound for ~(λ1)(G) when each edge of G belongs to at least t(t<1) triangles. Some new upper and lower bounds on ~(q1)(G), ~(q1)(G)+~(q1)(Gc) are determined, respectively. We also compare our results in this paper with some ...
In this paper, we first present a new upper bound for λ 1 ( G ) when each edge of G belongs to at least t ( t ≥ 1 ) triangles. Some new upper and lower bounds on q 1 ( G ), q 1 ( G ) + q 1 ( G c ) are determined, respectively. We also compare our results in ...
At last, we characterize the unique graph having the maximum spectral radius among the set of n n -vertex non-bipartite graphs with odd girth at least 2k+3, 2k+3, which solves an open problem proposed by Lin, Ning and Wu [Eigenvalues and triangles in graphs, Combin. Probab. Comput. ...
This includes the so-called friendship graphs, which consist of a number of edge-disjoint triangles meeting in one vertex. It turns out that the friendship graph is determined by its spectrum, except when the number of triangles equals sixteen....