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Suppose $G$ is a undirected simple graph. A $k-$subset of edges in $G$ without common vertices is called a $k-$matching and the number of such subsets is denoted by $p(G,k)$. The aim of this paper is to present exact formulas for $p(G,3)$, $p(G,4)$ a
Externí odkaz:
http://arxiv.org/abs/2107.04322
Autor:
Das, Kinkar Ch., Mojallal, Seyed Ahmad
Let $G$ be a graph of order $n$ with $m$ edges. Also let $\mu_1\geq \mu_2\geq \cdots\geq \mu_{n-1}\geq \mu_n=0$ be the Laplacian eigenvalues of graph $G$ and let $\sigma=\sigma(G)$ $(1\leq \sigma\leq n)$ be the largest positive integer such that $\mu
Externí odkaz:
http://arxiv.org/abs/1711.06906
A graph is almost self-centered (ASC) if all but two of its vertices are central. An almost self-centered graph with radius $r$ is called an $r$-ASC graph. The $r$-ASC index $\theta_r(G)$ of a graph $G$ is the minimum number of vertices needed to be
Externí odkaz:
http://arxiv.org/abs/1709.00589
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
Externí odkaz:
http://arxiv.org/abs/1705.07419
The Kirchhoff index $Kf(G)$ of a graph $G$ is the sum of resistance distances between all unordered pairs of vertices, which was introduced by Klein and Randi\'c. In this paper we characterized all extremal graphs with Kirchhoff index among all graph
Externí odkaz:
http://arxiv.org/abs/1602.07039
Let $G$ be a connected graph of order $n$ with diameter $d$. Remoteness $\rho$ of $G$ is the maximum average distance from a vertex to all others and $\partial_1\geq\cdots\geq \partial_n$ are the distance eigenvalues of $G$. In \cite{AH}, Aouchiche a
Externí odkaz:
http://arxiv.org/abs/1507.07083
Autor:
Das, Kinkar Ch., Mojallal, Seyed Ahmad
Publikováno v:
Taiwanese Journal of Mathematics, 2019 Oct 01. 23(5), 1041-1059.
Externí odkaz:
https://www.jstor.org/stable/26787549
Publikováno v:
In Discrete Mathematics June 2019 342(6):1718-1730
Publikováno v:
In Linear Algebra and Its Applications 15 May 2019 569:266-284