English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Suppose that the vertex set of a connected graph $G$ is$V(G)=\{v_1,\cdots,v_n\}$. Then we denote by $Tr_{G}(v_i)$ the sum of distancesbetween $v_i$ and all other vertices of $G$. Let $Tr(G)$ be the $n\times n$diagonal matrix with its $(i,i)$-entry equal to $Tr_{G}(v_{i})$ and $D(G)$ bethe distance matrix of $G$. Then $Q_{D}(G)=Tr(G)+D(G)$ and$L_{D}(G)=Tr(G)-D(G)$ are respectively the distance signless Laplacian matrixand distance Laplacian matrix of $G$. The largest eigenvalues $\rho_{Q}(G)$ and$\rho_{L}(G)$ of $Q_D(G)$ and $L_D(G)$ are respectively called distancesignless Laplacian spectral radius and distance Laplacian spectral radius of$G$. In this paper we give some graft transformations and use them tocharacterize the tree $T$ such that $\rho_{Q}(T)$ and $\rho_{L}(T)$ attain themaximum among all trees of order $n$ with given number of pendant vertices.

Some graft transformations and their applications on distance (signless) Laplacian spectra of graphs