Spectra of variants of distance matrices of graphs and digraphs: a survey
, 2021 Distance matrices of graphs were introduced by Graham and Pollack in 1971 to study a problem in communications. Since then, there has been extensive research on the distance matrices of graphs -- a 2014 survey by Aouchiche and Hansen on spectra of ...
Hogben, Leslie, Reinhart, Carolyn
core
Multi-attribute decision-making for electronic waste recycling using interval-valued Fermatean fuzzy Hamacher aggregation operators. [PDF]
Granul Comput, 2023 Luqman A, Shahzadi G.
europepmc +1 more source
Graph functions maximized on a path
, 2015 Given a connected graph G of order n and a nonnegative symmetric matrix A=[ai,j] of order n, define the function FA(G) as FA(G)=Σ1≤iG(i,j)ai,j, where dG(i,j) denotes the distance between the vertices i and j in G. In this note it is shown that FA(G)≤FA(P)
Nikiforov, Vladimir +1 more
core +1 more source
Coalescing sets preserving cospectrality of graphs arising from block similarity matrices
Coalescing involves gluing one or more rooted graphs onto another graph. Under specific conditions, it is possible to start with cospectral graphs that are coalesced in similar ways that will result in new cospectral graphs.
Mahamud, Sajid Bin +7 more
core +2 more sources
O espectro da matriz distância de uma família de grafos distância-birregulares
, 2023 É sabido que para um grafo conexo qualquer, a quantidade de autovalores distintos da sua matriz de adjacência é pelo menos o valor do diâmetro do grafo mais um, valendo o mesmo para as matrizes Laplaciana e Laplaciana sem sinal.
Silva, Tayná Lobo da
core
Деякі оцінки для лапласіанового енергоподібного інваріанта із беззнаковою відстанню у мережах
For a graph or network $G$, denote by $D(G)$ the distance matrix and $Tr(G)$ the diagonal matrix of vertex transmissions. The distance signless Laplacian matrix of $G$ is $D^{Q}(G)=Tr(G)+D(G)$.
Pirzada, S. +3 more
core +1 more source
3-partite Turán graphs due to edge deletion the change of distance signless Laplacian energy
Euler tarafından yapılan çalışmayla veya en yaygın bilinen haliyle Könisberg Köprü Problemi ile başlayan graf teorinin oldukça yaygın kullanım alanları vardır.
Öznalcılar, Betül Sena
core
Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph. [PDF]
J Inequal Appl, 2018 Jia H, Song H.
europepmc +1 more source
Characterizing path-factor deleted graphs via
A graph G has a P≥k-factor if G has a spanning subgraph H such that every component of H is a path of order at least k. A graph G is P≥k-factor deleted if G − e has a P≥k-factor for each edge e ∈ E(G).
Jianxi Li, Xiaoyun Lv, Shou-Jun Xu
core +1 more source
Some properties of generalized distance eigenvalues of graphs
summary:Let $G$ be a simple connected graph with vertex set $V(G)=\{v_1,v_2,\dots ,v_n \}$ and edge set $E(G)$, and let $d_{v_{i}}$ be the degree of the vertex $v_i$. Let $D(G)$ be the distance matrix and let $T_r(G)$ be the diagonal matrix of the vertex
Ma, Yuzheng, Shao, Yanling
core +1 more source