OmpU is a multimeric, cation selective outer membrane protein of Vibrio and related species that non-covalently interact with peptidoglycan layer. Interaction of OmpU with human host cells triggers ...signaling pathways to promote cytokine secretion, reactive oxygen species production, and caspase independent death in immune and epithelial cells. Non-choleric OmpU imparts resistance to antimicrobial peptides and induces actin cytoskeletal reorganization in the host cells. Further, OmpU isolated from Vibrio species elicits an immune response in several aquaculture hosts. Importantly, in-vivo studies using recombinant OmpU or OmpU derived mimotopes reveal a short-lasting immunity, and protection against Vibrio in the aquaculture sector. In conclusion, OmpU is a key adhesion protein and an important virulence factor for successful colonization of Vibrio species into hosts. This review article provides a broad overview of structural, regulatory, and functional mechanisms of OmpU in normal and disease states.
●Outer Membrane Proteins (OMPs) are important adhesion factors that play a role in host colonization and evasion of host defense.●OmpU, the most abundant and conserved outer membrane protein among Vibrio species, induces proinflammatory response and apoptosis in host cells.●OmpU activates receptor-mediated pathways in several target cells and enters the cell via clathrin dependent endocytosis.●OmpU, a strong immunogen, has a potential to protect non-choleric infection in the aquaculture sector.
Let D be a digraph with n vertices and a arcs. The Laplacian and the signless Laplacian matrices of D are, respectively, defined as L(D)=Deg+(D)−A(D) and Q(D)=Deg+(D)+A(D), where A(D) represents the ...adjacency matrix and Deg+(D) represents the diagonal matrix whose diagonal elements are the out-degrees of the vertices in D. We derive a combinatorial representation regarding the first few coefficients of the (signless) Laplacian characteristic polynomial of D. We provide concrete directed motifs to highlight some applications and implications of our results. The paper is concluded with digraph examples demonstrating detailed calculations.
For a simple graph G of order n, size m and with signless Laplacian eigenvalues q1,q2,…,qn, the signless Laplacian energy QE(G) is defined as QE(G)=∑i=1n|qi−d‾|, where d‾=2mn is the average vertex ...degree of G. We obtain the lower bounds for QE(G), in terms of first Zagreb index M1(G), maximum degree d1, second maximum degree d2, minimum degree dn and second minimum degree dn−1. As a consequence of these bounds, we obtain several bounds for the energy E(L(G)) of the line graph L(G) of graph G in terms of various graph parameters like M1(G), ω (the clique number), n, m, etc., which improve some recently known bounds.
Let G be a simple connected graph. In this paper, we study the spectral properties of the generalized distance matrix of graphs, the convex combination of the symmetric distance matrix D ( G ) and ...diagonal matrix of the vertex transmissions T r ( G ) . We determine the spectrum of the join of two graphs and of the join of a regular graph with another graph, which is the union of two different regular graphs. Moreover, thanks to the symmetry of the matrices involved, we study the generalized distance spectrum of the graphs obtained by generalization of the join graph operation through their eigenvalues of adjacency matrices and some auxiliary matrices.
Let D be a digraph of order n and let
be the adjacency matrix of D. Let
be the diagonal matrix of vertex out-degrees of D. For any real
, the generalized adjacency matrix
of the digraph D is defined ...as
The largest modulus of the eigenvalues of
is called the generalized adjacency spectral radius or the
-spectral radius of D. In this paper, we obtain some lower bounds for the spectral radius of
in terms of the number of vertices, the number of arcs and the number of closed walks of the digraph D. The extremal graphs attained these lower bounds are determined. We also obtain some bounds for the spectral radius of
in terms of the vertex out-degrees, the vertex average 2-out-degrees of the vertices of D and parameter α. We characterize the extremal digraphs attaining these bounds.
For a simple graph G with n-vertices, m edges and having signless Laplacian eigenvalues q1,q2,…,qn, the signless Laplacian energy QE(G) of the graph G is defined as QE(G)=∑i=1n∣qi−d¯∣, where d¯=2mn ...is the average degree of G. In this paper, we obtain the lower and upper bounds for the signless Laplacian energy QE(G) in terms of clique number ω, maximum degree Δ, number of vertices n, first Zagreb index M1(G) and number of edges m. As an application, we obtain the bounds for the energy of line graph ℒ(G) of a graph G in terms of various graph parameters. We also obtain a relation between the signless Laplacian energy QE(G) and the incidence energy IE(G).
Let D be a digraph of order n and with a arcs. The signless Laplacian matrix Q(D) of D is defined as Q(D)=Deg(D)+A(D), where A(D) is the adjacency matrix and Deg(D) is the diagonal matrix of vertex ...out-degrees of D. Among the eigenvalues of Q(D) the eigenvalue with largest modulus is the signless Laplacian spectral radius or the Q-spectral radius of D. The main contribution of this paper is a series of new lower bounds for the Q-spectral radius in terms of the number of vertices n, the number of arcs, the vertex out-degrees, the number of closed walks of length 2 of the digraph D. We characterize the extremal digraphs attaining these bounds. Further, as applications we obtain some bounds for the signless Laplacian energy of a digraph D and characterize the extremal digraphs for these bounds.
Digraphs; Strongly connected digraphs; Signless Laplacian spectral radius; Generalized adjacency spectral radius; Energy
Let G be a simple graph with order n and size m and having Laplacian eigenvalues μ1,μ2,…,μn−1,μn=0 and let Sk(G)=∑i=1kμi be the sum of k largest Laplacian eigenvalues of G. Brouwer conjectured that ...Sk(G)≤m+(k+12), for all k=1,2,…,n. We obtain upper bounds for Sk(G), in terms of the clique number ω, the order n and integers p≥0,r≥1,s1≥s2≥2 associated to the structure of the graph G. We discuss Brouwer's conjecture for two large families of graphs; the first family of graphs is obtained from a clique of size ω by identifying each of its vertices to a vertex of an arbitrary c-cyclic graph, and the second family is composed of the graphs in which the removal of the edges of the maximal complete bipartite subgraph gives a graph each of whose non-trivial components is a c-cyclic graph. We show among these two large families of graphs, the Brouwer's conjecture holds for various subfamilies of graphs depending upon the value of c, the order of the c-cyclic graphs, the clique number of the graph, the order of the maximal complete bipartite subgraph and the number of the c-cyclic components of the graph.
On generalized distance energy of graphs Pirzada, S.; Ganie, Hilal A.; Rather, Bilal A. ...
Linear algebra and its applications,
10/2020, Volume:
603
Journal Article
Peer reviewed
For the distance matrix D(G) and diagonal matrix of the vertex transmissions Tr(G) of a simple connected graph G, the generalized distance matrix Dα(G) is the convex combinations of Tr(G) and D(G), ...and is defined as Dα(G)=αTr(G)+(1−α)D(G), for 0≤α≤1. If ∂1≥∂2≥…≥∂n are the eigenvalues of Dα(G), we define the generalized distance energy of the graph G as EDα(G)=∑i=1n|∂i−2αW(G)n|, where W(G) is the Wiener index of G. This is analogous to the energies associated with the distance Laplacian and distance signless Laplacian matrices of G. We obtain upper and lower bounds for the generalized distance energy of graphs, in terms of various parameters associated with the structure of the graph G. We show that for α∈12,1), the complete bipartite graph has the minimum generalized distance energy among all connected bipartite graphs, and for α∈(0,2n3n−2), the star graph has the minimum generalized distance energy among all trees.
Let G be a simple connected graph with n vertices, m edges and having distance signless Laplacian eigenvalues
. For
, let
and
be respectively the sum of k-largest distance signless Laplacian ...eigenvalues and the sum of k-smallest distance signless Laplacian eigenvalues of G. In this paper, we obtain the bounds for
and
in terms of the number of vertices n and the transmission
of the graph G. We propose a Brouwer-type conjecture for
and show that it holds for graphs of diameter one and graphs of diameter two for all k. As a consequence, we observe that the conjecture holds for threshold graphs and split graphs (of diameter two). We also show that it holds for k = n−1 and n for all graphs and for some k for r-transmission regular graphs.
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