Constructing cospectral graphs
WebAug 10, 2024 · Download PDF Abstract: Construction of non-isomorphic cospectral graphs is a nontrivial problem in spectral graph theory specially for large graphs. In this paper, we establish that graph theoretical partial transpose of a graph is a potential tool to create non-isomorphic cospectral graphs by considering a graph as a clustered graph. WebApr 7, 2024 · A switching method for constructing cospectral gain graphs. A gain graph over a group , also referred to as -gain graph, is a graph where an element of a group , called gain, is assigned to each oriented edge, in such a way that the inverse element is associated with the opposite orientation. Gain graphs can be regarded as a …
Constructing cospectral graphs
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WebOct 1, 2024 · Constructing cospectral non-isomorphic graphs provides valuable insights to understanding the above question. For an instance, a famous result on cospectral … WebVol. 25, 1982 Constructing cospectral graphs 259 (a) OZ =/~. (b) If X is an m x n matrix with constant row sums and constant column sums, then QmXQ~ = X. (c) If x is a vector …
WebApr 7, 2024 · graphs [3] and complex unit graphs [4], and more recently, also to ga in graphs ov er an arbitrary group [8]. The W QH-switching has also been extended, in its … WebOct 15, 2024 · In Section 3, we present a family of infinitely many cospectral graphs by using the new method, which cannot be obtained from the original GM-switching. …
Webin spectral graph theory, and hence, methods for constructing cospectral graphs are of interest. To date, such construction methods have mainly fallen into two categories. The … WebAug 6, 2024 · 摘要： A well--known fact in Spectral Graph Theory is the existence of pairs of isospectral nonisomorphic graphs (known as PINGS). The work of A.J. Schwenk (in 1973) and of C. Godsil and B. McKay (in 1982) shed some light on the explanation of the presence of isospectral graphs, and they gave routines to construct PINGS.
WebApr 1, 2010 · Applying these results we construct some non-regular A-cospectral, L-cospectral and L-cospectral graphs which gives a partial answer of the question asked by Butler [2]. Moreover, we determine the ...
WebAug 6, 2024 · Constructing cospectral signed graphs. A well--known fact in Spectral Graph Theory is the existence of pairs of isospectral nonisomorphic graphs (known as PINGS). The work of A.J. Schwenk (in 1973) and of C. Godsil and B. McKay (in 1982) shed some light on the explanation of the presence of isospectral graphs, and they gave … economic system of great zimbabwe stateWebJun 30, 2024 · In this paper we introduce a simple method for constructing infinite families of cospectral regular graphs. The construction is valid for special cases of a property … conair flight that crashed in detroitWebOct 15, 2024 · The rest of the paper is organized as follows. In Section 2, we give a new method for constructing cospectral graphs which is analogous to the GM-switching method. In Section 3, we present a family of infinitely many cospectral graphs by using the new method, which cannot be obtained from the original GM-switching. Conclusions are … economic system of iranWebWorcester Polytechnic Institute (WPI) conair folding brushWebJan 1, 2024 · Two graphs G and H are cospectral if they share the same spectrum. Constructing cospectral non-isomorphic graphs has been investigated for many years and various constructions are known in the literature, among which, the GM-switching, invented by Godsil and McKay in 1982, is proved to a simple and powerful one. economic system in franceWebFeb 2, 2024 · Results that imply Theorem 2 appear in most books that treat graph spectra - note that the formula holds for all graphs, not just trees. Second, to extract coefficients, you need tools for manipulating power series. ... Are cospectral/non-cospectral non-isomorphic graphs similar? 11. Prove that all trees are bipartite. 3. conair folding lighted makeup mirrorWebAbstract We present a new method to construct a family of co-spectral graphs. Our method is based on a new type of graph product that we define, the bipartite graph product, which may be of self-interest. Our method is different from existing techniques in the sense that it is not based on a sequence of local graph operations (e.g. Godsil–McKay … conair foot vibes