Here, we are interested in two graph operations, namely, motif (subgraph) doubling and attachment that are biologically relevant. We investigate how these two processes affect the spectrum of the normalized graph Laplacian. A high (algebraic) multiplicity of the eigenvalues 1,1±0.5,1±0.5 and ...
On two energy-like invariants of line graphs and related graph operations Summary: For a simple graph $G$ of order $n$, let $μ_{1}\\\geqμ_{2}\\\geq\\\cdots\\\geqμ_{n}=0$ be its Laplacian eigenvalues, and let $q_{1}\\\geq ... X Chen,Y Hou,J Li - 《Journal of...
power graphfinite ringfinite groupIn this paper, we determine the distance Laplacian spectra of graphs obtained by various graph operations. We obtain the distance Laplacian spectrum of the join of two graphsG1andG2in terms of adjacency spectra ofG1andG2. Then we obtain the distance Laplacian ...
ADJACENCY AND LAPLACIAN SPECTRA OF NEW GRAPH OPERATIONS BASED ON INDU-BALA PRODUCT OF GRAPHSPHUKAN, BABLEEGOGOI, IDWEEP J.BHARALI, A.Journal of Advanced Mathematical Studies
The result shows that the symmetric normalized Laplacian matrix is suitable for denser graphs, while the random walk normalized Laplacian matrix is more feasible for sparser graph-based operations.Dai, ChuanUniversity of HuddersfieldWei, Yajuan
We investigate how the spectrum of the normalized (geometric) graph Laplacian is affected by operations like motif dougling, graph splitting or joining. The multiplicity of the eigenvalue 1, or equivalently, the dimension of the kernel of the adjacency matrix of the graph is of particular ...
(SOM)introduces lateral interaction in a general form in which signals of any modality can be used.Some approaches directly incorporate SOM learning rules into neural networks,but incur complex operations and poor extendibility.The efficient way to implement lateral interaction in deep neur...
A formula has also been created to make our application's basic operations more understandable.S. N. Suber Bathushahttps://ror.org/02qgw5c67grid.411780.b0000 0001 0683 3327Department of Mathematics, Sadakathullah Appa CollegeAffiliated to Manonmaniam Sundaranar University Abishekapatti 627012 Ti...
GrmnthenQ(G)@?GrmnandL(@l, G)@?L(@l,Q(G))for@l@?n.Because of the relationt(K"s\\E(G"n)) =srs-n-2L(s,G"n) [5],these operations also increase the number of spanning trees of the corresponding complement graphs:t(K"s\\E(G)) @? t(K"s\\E(Q(G)).The approach ...
math} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ho(\\mathcal{L}(G))$$\\end{document}when the graph is perturbed by three operations....