Results 51 to 60 of about 41,123 (303)
On distance-regularity in graphs
Journal of Combinatorial Theory, Series B, 1982 AbstractIf A is the adjacency matrix of a graph G, then Ai is the adjacency matrix of the graph on the same vertex set in which a pair of vertices is adjacent if and only if their distance apart is i in G. If G is distance-regular, then Ai is a polynomial of degree i in A. It is shown that the converse is also true.
openaire +1 more source
The pseudo-cosine sequences of a distance-regular graph [PDF]
, 2006 Let Γ denote a distance-regular graph with diameter D⩾3, valency k, and intersection numbers ai, bi, ci. By a pseudo-cosine sequence of Γ we mean a sequence of real numbers σ0,σ1,…,σD such that σ0=1 and ciσi−1+aiσi+biσi+1=kσ1σi for 0⩽i⩽D−1.
Pascasio, Arlene A., Terwilliger, Paul
core +1 more source
The Q-polynomial idempotents of a distance-regular graph [PDF]
, 2010 We obtain the following characterization of Q-polynomial distance-regular graphs. Let Γ denote a distance-regular graph with diameter d⩾3. Let E denote a minimal idempotent of Γ which is not the trivial idempotent E0.
Paul Terwilliger +5 more
core +1 more source
Ural Mathematical JournalWe consider antipodal graphs \(\Gamma\) of diameter 4 for which \(\Gamma_{1,2}\) is a strongly regular graph. A.A. Makhnev and D.V. Paduchikh noticed that, in this case, \(\Delta=\Gamma_{3,4}\) is a strongly regular graph without triangles.
Alexander A. Makhnev +2 more
doaj +1 more source
Sharp Bounds on (Generalized) Distance Energy of Graphs
Mathematics, 2020 Given a simple connected graph G, let D ( G ) be the distance matrix, D L ( G ) be the distance Laplacian matrix, D Q ( G ) be the distance signless Laplacian matrix, and T r ( G ) be the vertex transmission ...
Abdollah Alhevaz +3 more
doaj +1 more source
Distance-Regular Graphs and Halved Graphs
European Journal of Combinatorics, 1986 Let G be a bipartite distance-regular graph with bipartition \(V(G)=X\cup Y\). Let \(V(G')=X\) and, for x and y in X, let x be adjacent to y in G' if and only if x is of distance two from y in G. Then G' is called a halved graph of G, and is distance-regular. This paper discusses whether G' is one of the known, large-diameter, distance-regular graphs.
openaire +2 more sources
FEBS Letters, EarlyView.Septin 9 polybasic domains couple phosphoinositide‐rich membrane binding to centrosome positioning, Golgi organization, and microtubule acetylation to control epithelial polarity. Their loss disrupts this axis, causing centrosome mispositioning, Golgi fragmentation, reduced microtubule acetylation, and polarity inversion via upregulation of the ...
Ting ting Cai +4 more
wiley +1 more source
IEEE Access, 2018 The resistance distance is widely used in random walk, electronic engineering, and complex networks. One of the main topics in the study of the resistance distance is the computation problem.
Qun Liu, Jia-Bao Liu, Shaohui Wang
doaj +1 more source
Ural Mathematical Journal, 2021 The vertex distance complement (VDC) matrix \(\textit{C}\), of a connected graph \(G\) with vertex set consisting of \(n\) vertices, is a real symmetric matrix \([c_{ij}]\) that takes the value \(n - d_{ij}\) where \(d_{ij}\) is the distance between the
Ann Susa Thomas +2 more
doaj +1 more source
FEBS Letters, EarlyView.This study reveals that the small GTPase Rab14 is necessary for human papillomavirus (HPV) infection and plays an essential role in the transport of virions to the trans‐Golgi network (TGN). HPV in the early endosome (EE), which harbors GTP‐bound Rab14, is transported to the TGN through the switch of Rab14 from its GTP‐bound to GDP‐bound form.
Yoshiyuki Ishii, Iwao Kukimoto
wiley +1 more source