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pro vyhledávání: '"Ghalavand Ali"'
The local metric dimension ${\rm dim}_l$ in relation to the clique number $\omega$ is investigated. It is proved that if $\omega(G)\leq n(G)-3$, then ${\rm dim}_l(G) \leq n(G)-3$ and the graphs attaining the bound classified. Moreover, the graphs $G$
Externí odkaz:
http://arxiv.org/abs/2412.17074
Publikováno v:
Kragujevac Journal of Science, Vol 2019, Iss 41, Pp 37-42 (2019)
In this paper, some inequalities between the Wiener, hyper-Wiener, first Zagreb, second Zagreb, first reformulated Zagreb, second reformulated Zagreb and the general Zagreb indices of a simple graph are given. Our results improve some earlier bonds b
Externí odkaz:
https://doaj.org/article/637e83e007034b6daf39a64daf3993dc
The mixed metric dimension ${\rm mdim}(G)$ of a graph $G$ is the cardinality of a smallest set of vertices that (metrically) resolves each pair of elements from $V(G)\cup E(G)$. We say that $G$ is a max-mdim graph if ${\rm mdim}(G) = n(G)$. It is pro
Externí odkaz:
http://arxiv.org/abs/2305.19620
In this study we are interested mainly in investigating the relations between two graph irregularity measures which are widely used for structural irregularity characterization of connected graphs. Our study is focused on the comparison and evaluatio
Externí odkaz:
http://arxiv.org/abs/2211.06744
Let $G$ be a graph and let $S(G)$, $M(G)$, and $T(G)$ be the subdivision, the middle, and the total graph of $G$, respectively. Let ${\rm dim}(G)$, ${\rm edim}(G)$, and ${\rm mdim}(G)$ be the metric dimension, the edge metric dimension, and the mixed
Externí odkaz:
http://arxiv.org/abs/2206.04983
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:
Ghalavand, Ali, Ashrafi, Ali Reza
Let $G$ be a finite simple graph with Laplacian polynomial $\psi(G,\lambda)=\sum_{k=0}^n(-1)^{n-k}c_k\lambda^k$. In an earlier paper, the coefficients $c_{n-4}$ and $c_{n-5}$ for tree with respect to some degree-based graph invariants were computed.
Externí odkaz:
http://arxiv.org/abs/2104.08476
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. The Sombor and reduced Sombor indices of $G$ are defined as $SO(G)=\sum_{uv\in E(G)}\sqrt{deg_G(u)^2+deg_G(v)^2}$ and $SO_{red}(G)=\sum_{uv\in E(G)}\sqrt{(deg_G(u)-1)^2+(deg_G(v)-1)^2}$,
Externí odkaz:
http://arxiv.org/abs/2103.17147
Autor:
Ghalavand, Ali, Ashrafi, Ali Reza
Let G be an n-vertex graph with m edges. The degree deviation measure of G is defined as s(G)=sum v in V(G)|degG(v)-(2m/n)|, where n and m are the number of vertices and edges of G, respectively. The aim of this paper is to prove the Conjecture 4.2 o
Externí odkaz:
http://arxiv.org/abs/2002.09020
Suppose $G$ is a simple graph with edge set $E(G)$. The Randi\'{c} index $R(G)$ is defined as $R(G)=\sum_{uv\in E(G)}\frac{1}{\sqrt{deg_{G}(u)deg_{G}(v)}}$, where $deg_G(u)$ denotes the vertex degree of $u$ in $G$. In this paper, the first and second
Externí odkaz:
http://arxiv.org/abs/1907.10996