Results 21 to 30 of about 80 (69)
On the Largest Distance (Signless Laplacian) Eigenvalue of Non-transmission-regular Graphs
The Electronic Journal of Linear Algebra, 2018 Let $G=(V(G),E(G))$ be a $k$-connected graph with $n$ vertices and $m$ edges. Let $D(G)$ be the distance matrix of $G$. Suppose $\lambda_1(D)\geq \cdots \geq \lambda_n(D)$ are the $D$-eigenvalues of $G$. The transmission of $v_i \in V(G)$, denoted by $Tr_G(v_i)$ is defined to be the sum of distances from $v_i$ to all other vertices of $G$, i.e., the ...
Liu, Shuting, Shu, Jinlong, Xue, Jie
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Resistance Distance and Kirchhoff Index for a Class of Graphs
Mathematical Problems in Engineering, Volume 2018, Issue 1, 2018., 2018 Let G[F, Vk, Hv] be the graph with k pockets, where F is a simple graph of order n ≥ 1, Vk = {v1, v2, …, vk} is a subset of the vertex set of F, Hv is a simple graph of order m ≥ 2, and v is a specified vertex of Hv. Also let G[F, Ek, Huv] be the graph with k edge pockets, where F is a simple graph of order n ≥ 2, Ek = {e1, e2, …ek} is a subset of the ...
WanJun Yin +3 more
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Generalized Characteristic Polynomials of Join Graphs and Their Applications
Discrete Dynamics in Nature and Society, Volume 2017, Issue 1, 2017., 2017 The Kirchhoff index of G is the sum of resistance distances between all pairs of vertices of G in electrical networks. LEL(G) is the Laplacian‐Energy‐Like Invariant of G in chemistry. In this paper, we define two classes of join graphs: the subdivision‐vertex‐vertex join G1⊚G2 and the subdivision‐edge‐edge join G1⊝G2.
Pengli Lu +3 more
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Bounds on the Spectral Radius of a Nonnegative Matrix and Its Applications
Journal of Applied Mathematics, Volume 2016, Issue 1, 2016., 2016 We obtain the sharp bounds for the spectral radius of a nonnegative matrix and then obtain some known results or new results by applying these bounds to a graph or a digraph and revise and improve two known results.
Danping Huang, Lihua You, Ali R. Ashrafi
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Ain Shams Engineering JournalIn this study, we define the structure formation of the annihilator monic prime graph of commutative rings, whose distinct vertices X and J satisfies a condition annXJ≠annX⋃ann(J), graph is denoted by AMPG(Zn[x]/〈fx〉).
R. Sarathy, J. Ravi Sankar
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The Least Algebraic Connectivity of Graphs
Discrete Dynamics in Nature and Society, Volume 2015, Issue 1, 2015., 2015 The algebraic connectivity of a graph is defined as the second smallest eigenvalue of the Laplacian matrix of the graph, which is a parameter to measure how well a graph is connected. In this paper, we present two unique graphs whose algebraic connectivity attain the minimum among all graphs whose complements are trees, but not stars, and among all ...
Guisheng Jiang +3 more
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The Largest Laplacian Spectral Radius of Unicyclic Graphs with Fixed Diameter
Journal of Applied Mathematics, Volume 2013, Issue 1, 2013., 2013 We identify graphs with the maximal Laplacian spectral radius among all unicyclic graphs with n vertices and diameter d.
Haixia Zhang, Baolin Wang
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The Electronic Journal of Linear Algebra, 2018 The \emph{distance matrix} of a simple connected graph $G$ is $D(G)=(d_{ij})$, where $d_{ij}$ is the distance between the $i$th and $j$th vertices of $G$. The \emph{distance signless Laplacian matrix} of the graph $G$ is $D_Q(G)=D(G)+Tr(G)$, where $Tr(G)$ is a diagonal matrix whose $i$th diagonal entry is the transmission of the vertex $i$ in $G$.
Atik, Fouzul, Panigrahi, Pratima
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Spectral Properties of the Harary Signless Laplacian and Harary Incidence Energy
MathematicsLet X be a partitioned matrix and let B its equitable quotient matrix. Consider a simple, undirected, connected graph G of order n. In this paper, we employ a technique based on quotient matrices derived from block-partitioned structures to establish new
Luis Medina +2 more
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More results on the distance (signless) Laplacian eigenvalues of graphs
, 2017 Let $G$ be a connected graph with vertex set $V(G)$ and edge set $E(G)$. Let $Tr(G)$ be the diagonal matrix of vertex transmissions of $G$ and $D(G)$ be the distance matrix of $G$. The distance Laplacian matrix of $G$ is defined as $\mathcal{L}(G)=Tr(G)-D(G)$. The distance signless Laplacian matrix of $G$ is defined as $\mathcal{Q}(G)=Tr(G)+D(G)$.
Xue, Jie +3 more
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