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ON THE MATCHING NUMBER OF AN UNCERTAIN GRAPH
, 2017Summary: Uncertain graphs are employed to describe graph models with indeterministic information that produced by human beings. This paper aims to study the maximum matching problem in uncertain graphs. The number of edges of a maximum matching in a graph is called matching number of the graph.
Hui Li, Bo Zhang, Jin Peng
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An improved lower bound for the nullity of a graph in terms of matching number
Linear and multilinear algebra, 2020Let G be a connected undirected graph without loops and multiple edges. By , and we, respectively, denote the order, the nullity, and the matching number of G. Let , and let be a nonnegative integer defined as: To make G to be a bipartite connected graph
Xiaobin Ma, Xianwen Fang
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Linear and multilinear algebra, 2020
Let be an n-vertex complex unit gain graph and let G be its underlying graph. The adjacency rank of , written as , is the rank of its adjacency matrix and denote by the matching number of the underlying graph G.
Shuchao Li, Ting Yang
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Let be an n-vertex complex unit gain graph and let G be its underlying graph. The adjacency rank of , written as , is the rank of its adjacency matrix and denote by the matching number of the underlying graph G.
Shuchao Li, Ting Yang
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The Kirchhoff index and the matching number
International Journal of Quantum Chemistry, 2008AbstractThe Kirchhoff index of a connected (molecular) graph is the sum of the resistance‐distances between all unordered pairs of vertices and may also be expressed by its Laplacian eigenvalues. We determine the minimum Kirchhoff index of connected (molecular) graphs in terms of the number of vertices and matching number and characterize the unique ...
Zhou, Bo, Trinajstic, Nenad
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Relationship between the rank and the matching number of a graph
Applied Mathematics and Computation, 2019Given a simple graph G, let A(G) be its adjacency matrix and α′(G) be its matching number. The rank of G, written as r(G), refers to the rank of A(G). In this paper, some relations between the rank and the matching number of a graph are studied. Firstly,
Zhi-Ming Feng +3 more
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Resilient Hypergraphs with Fixed Matching Number
Combinatorica, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
P. Frankl
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On Neighbourhood Matching for Texture‐by‐Numbers
Computer Graphics Forum, 2010Abstract Texture‐by‐Numbers is an attractive texture synthesis framework, because it is able to cope with non‐homogeneous texture exemplars, and provides the user with intuitive creative control over the outcome of the synthesis process. Like many other exemplar‐based texture synthesis methods, its basic underlying mechanism is neighbourhood matching ...
Eliyahu Sivaks, Dani Lischinski
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Matching number, connectivity and eigenvalues of distance signless Laplacians
Linear and multilinear algebra, 2019Let G be a connected graph. The first and the second largest distance signless Laplacian eigenvalues of G are denoted by and . In this paper, we determine the graphs with the minimum among n-vertex graphs with given matching number.
Shuchao Li, Wanting Sun
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The fractional matching numbers of graphs
Networks, 2002AbstractA fractional matching of a graph G is a function f that assigns to each edge a number in [0, 1] such that, for each vertex v, ∑ f(e) ≤ 1, where the sum is taken over all edges incident to v. The fractional matching number of G is the supremum of ∑e∈E(G) f(e) over all fractional matchings f.
Yan Liu, Guizhen Liu
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Fractional matching number and eigenvalues of a graph
Linear and multilinear algebra, 2018A fractional matching of a graph G is a function f giving each edge a number in so that for each , where is the set of edges incident to v. The fractional matching number of G, written , is the maximum of over all fractional matchings.
Jie Xue, M. Zhai, Jin-Long Shu
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