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The matching number and Hamiltonicity of graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 The matching number of a graph G is the size of a maximum matching in the graph. In this note, we present a sufficient condition involving the matching number for the Hamiltonicity of graphs.
Rao Li
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Discontinuity and diversity of Persian scientific research journals in the field of educational sciences by using coloring and mathematical algebraic parameters [PDF]
ریاضی و جامعه, 2022 The aim of the current research is to study and compare graphs authorship by Iranian researchers in Persian scientific research journals in the field of educational sciences by using algebraic parameters of mathematics. In this research, the data related
Ali Abdi, Mostafa Amini
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Mathematics, 2022 A two-mode network is a type of network in which nodes can be divided into two sets in such a way that links can be established between different types of nodes. The relationship between two separate sets of entities can be modeled as a bipartite network.
Ali Al Khabyah +4 more
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Bounds on the Minimum Edge Dominating Energy in Terms of Some Parameters of a Graph [PDF]
Mathematics Interdisciplinary Research, 2023 The minimum edge dominating energy, denoted by $EE_{F}(G)$, is the sum of the absolute values of eigenvalues of the minimum edge dominating matrix of graph $G$.
Fateme Movahedi
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Extremal Graphs for Sombor Index with Given Parameters
Axioms, 2023 In this paper, we present the upper and lower bounds on Sombor index SO(G) among all connected graphs (respectively, connected bipartite graphs). We give some sharp lower and upper bounds on SO(G) among connected graphs in terms of some parameters ...
Wanping Zhang, Jixiang Meng, Na Wang
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On the Number of k-Matchings in Graphs
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2022 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 $p(G,3)$, $p(G,4)$ and $P(G,5)$ in terms of some degree-based invariants.
Kinkar Chandra Das +2 more
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A note on the size Ramsey numbers for matchings versus cycles [PDF]
Mathematica Bohemica, 2021 For graphs $G$, $F_1$, $F_2$, we write $G \rightarrow(F_1, F_2)$ if for every red-blue colouring of the edge set of $G$ we have a red copy of $F_1$ or a blue copy of $F_2$ in $G$.
Edy Tri Baskoro, Tomáš Vetrík
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New Results Relating Independence and Matchings
Discussiones Mathematicae Graph Theory, 2022 In this paper we study relationships between the matching number, written µ(G), and the independence number, written α(G).
Caro Yair, Davila Randy, Pepper Ryan
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On the Number of Matchings in Regular Graphs [PDF]
The Electronic Journal of Combinatorics, 2008 For the set of graphs with a given degree sequence, consisting of any number of $2's$ and $1's$, and its subset of bipartite graphs, we characterize the optimal graphs who maximize and minimize the number of $m$-matchings. We find the expected value of the number of $m$-matchings of $r$-regular bipartite graphs on $2n$ vertices with respect to the two ...
Shmuel Friedland +2 more
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A Short Proof of the Size of Edge-Extremal Chordal Graphs
Journal of Mathematical Sciences and Modelling, 2022 [3] have recently determined the maximum number of edges of a chordal graph with a maximum degree less than $d$ and the matching number at most $\nu$ by exhibiting a family of chordal graphs achieving this bound. We provide simple proof of their result.
Mordechai Shalom
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