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Entropy of Weighted Graphs With Randi´c Weights [PDF]
Entropy, 2015 Shannon entropies for networks have been widely introduced. However, entropies for weighted graphs have been little investigated. Inspired by the work due to Eagle et al., we introduce the concept of graph entropy for special weighted graphs. Furthermore, we prove extremal properties by using elementary methods of classes of weighted graphs, and in ...
Matthias Dehmer +2 more
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Graphs and Combinatorics, 2001
A perfectly weighted graph is a tree with integer weights \(n_1,\dots,n_k\geq 2\) on the vertices such that its dual intersection matrix (the diagonal matrix with entries \(n_1,\dots,n_k\) minus the adjacency matrix) is positive definite with determinant equal to 1. A tree is called perfectible if there are weights which make it a perfect graph.
Lawrence Brenton, Lynda Jaje
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A perfectly weighted graph is a tree with integer weights \(n_1,\dots,n_k\geq 2\) on the vertices such that its dual intersection matrix (the diagonal matrix with entries \(n_1,\dots,n_k\) minus the adjacency matrix) is positive definite with determinant equal to 1. A tree is called perfectible if there are weights which make it a perfect graph.
Lawrence Brenton, Lynda Jaje
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Combinatorica, 1991
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J. Adrian Bondy, Genghua Fan
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J. Adrian Bondy, Genghua Fan
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The threshold weight of a graph
Journal of Graph Theory, 1991AbstractThe threshold weight of a graph G is introduced as a measure of the amount by which G differs from being a threshold graph. The threshold graphs are precisely the graphs whose threshold weights are 0. At the opposite extreme is the class of graphs for which the threshold weight is the maximum possible.
Chi Wang 0002, A. C. Williams
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Weighted irredundance of interval graphs
Information Processing Letters, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Maw-Shang Chang +2 more
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Weighted Mean of a Pair of Graphs
Computing, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Horst Bunke, Simon Günter
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Ars Comb., 1998
The authors consider the graph weight \(w_\alpha (G)=\sum _{e\in E(G)}w_{\alpha }(e)\), where \(\alpha \neq 0\) is fixed and \(w_{\alpha }(e)=w_{\alpha }(\{x,y\})=(d(x)d(y))^\alpha \) with \(d(x)\) being the degree of \(x\). It is proved that for the Randić weight \(\alpha =-1/2\) (in the first definition in the article the ``\(-\)'' is missing), if ...
Béla Bollobás, Paul Erdös
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The authors consider the graph weight \(w_\alpha (G)=\sum _{e\in E(G)}w_{\alpha }(e)\), where \(\alpha \neq 0\) is fixed and \(w_{\alpha }(e)=w_{\alpha }(\{x,y\})=(d(x)d(y))^\alpha \) with \(d(x)\) being the degree of \(x\). It is proved that for the Randić weight \(\alpha =-1/2\) (in the first definition in the article the ``\(-\)'' is missing), if ...
Béla Bollobás, Paul Erdös
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On the spanning trees of weighted graphs
Combinatorica, 1989The paper deals with several natural questions that arise when the spanning trees of a weighted graph are partitioned into the weight classes. The authors prove that every minimum-weight spanning tree is at most \(k-1\) edge swaps away from some representative of the \(k\)-th weight class, thereby settling a conjecture of \textit{M.
Ernst W. Mayr, C. Greg Plaxton
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