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pro vyhledávání: '"05c07"'
We explore the fascinating world of Circumacenes, a unique family of organic molecules. Our research demonstrarates the calculation of essential topological indices, including the first and second-Zagreb indices, as well as related generalized indice
Externí odkaz:
http://arxiv.org/abs/2410.16313
Suppose $1 \le p \le \infty$. For a simple graph $G$ with a vertex-degree sequence $d_1, \dots, d_n$ satisfying $(d_1^p + \dots + d_n^p)^{1/p} \le C$, we prove asymptotically sharp upper bounds on the number of $t$-cliques in $G$. This result bridges
Externí odkaz:
http://arxiv.org/abs/2410.04744
A graph $G$ is $k$-critical (list $k$-critical, DP $k$-critical) if $\chi(G)= k$ ($\chi_\ell(G)= k$, $\chi_\mathrm{DP}(G)= k$) and for every proper subgraph $G'$ of $G$, $\chi(G')
Externí odkaz:
http://arxiv.org/abs/2410.01191
Autor:
Parui, Samiron
This study delves into the incidence matrices of hypergraphs, with a focus on two types: the edge-vertex incidence matrix and the vertex-edge incidence matrix. The edge-vertex incidence matrix is a matrix in which the rows represent hyperedges and th
Externí odkaz:
http://arxiv.org/abs/2409.16055
Autor:
Ai, Jiangdong, Ellingham, M. N., Gao, Zhipeng, Huang, Yixuan, Liu, Xiangzhou, Shan, Songling, Špacapan, Simon, Yue, Jun
Let $G$ be a graph (with multiple edges allowed) and let $T$ be a tree in $G$. We say that $T$ is $\textit{even}$ if every leaf of $T$ belongs to the same part of the bipartition of $T$, and that $T$ is $\textit{weakly even}$ if every leaf of $T$ tha
Externí odkaz:
http://arxiv.org/abs/2409.15522
Autor:
Long, Eoin, Ploscaru, Laurentiu
Given an $n$-vertex graph $G$, let $\hom (G)$ denote the size of a largest homogeneous set in $G$ and let $f(G)$ denote the maximal number of distinct degrees appearing in an induced subgraph of $G$. The relationship between these parameters has been
Externí odkaz:
http://arxiv.org/abs/2409.14134
We consider a Gibbs distribution over all spanning trees of an undirected, edge weighted finite graph, where, up to normalization, the probability of each tree is given by the product of its edge weights. Defining the weighted degree of a node as the
Externí odkaz:
http://arxiv.org/abs/2409.13472
Let $\mathscr{B}_n = \{ \pm x_1, \pm x_2, \pm x_3, \cdots, \pm x_{n-1}, x_n \}$ where $n>1$ is fixed, $x_i \in \mathbb{R}^+$, $i = 1, 2, 3, \cdots, n$ and $x_1 < x_2 < x_3 < \cdots < x_n$. Let $\phi(\mathscr{B}_n)$ be the set of all non-empty subsets
Externí odkaz:
http://arxiv.org/abs/2409.09317
Autor:
Vaidya, Sanju, Chang, Jeff
In the last forty years, many scientists used graph theory to develop mathematical models for analyzing structures and properties of various chemical compounds. In this paper, we will establish formulas and bounds for generalized first Zagreb Index a
Externí odkaz:
http://arxiv.org/abs/2409.06081
We show that every cubic graph on $n$ vertices contains a spanning subgraph in which the number of vertices of each degree deviates from $\frac{n}{4}$ by at most $\frac{1}{2}$, up to three exceptions. This resolves the conjecture of Alon and Wei (Irr
Externí odkaz:
http://arxiv.org/abs/2408.16121