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Discrete MathematicsWeighted Padovan graphs $Φ^{n}_{k}$, $n \geq 1$, $\lfloor \frac{n}{2} \rfloor \leq k \leq \lfloor \frac{2n-2}{3} \rfloor$, are introduced as the graphs whose vertices are all Padovan words of length $n$ with $k$ $1$s, two vertices being adjacent if one can be obtained from the other by replacing exactly one $01$ with a $10$. By definition, $\sum_k |V(Φ^
Vesna Iršič Chenoweth +3 more
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Total Weight Choosability of Graphs [PDF]
The Electronic Journal of Combinatorics, 2011 Suppose the edges and the vertices of a simple graph $G$ are assigned $k$-element lists of real weights. By choosing a representative of each list, we specify a vertex colouring, where for each vertex its colour is defined as the sum of the weights of its incident edges and the weight of the vertex itself.
Jakub Przybylo, Mariusz Wozniak
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Large scale clustering of protein sequences with FORCE - a layout based heuristic for weighted cluster editing [PDF]
, 2007 Wittkop T, Baumbach J, Lobo FP, Rahmann S. Large scale clustering of protein sequences with FORCE - a layout based heuristic for weighted cluster editing. BMC Bioinformatics.
Wittkop, Tobias +11 more
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Determinantal properties of Boolean graphs using recursive approach
AKCE International Journal of Graphs and CombinatoricsThe aim of this paper is to study the determinant and inverse of the adjacency matrices of weighted and directed versions of Boolean graphs. Our approach is recursive. We describe the adjacency matrix of a weighted Boolean graph in terms of the adjacency
Gahininath Sonawane +2 more
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Discrete Mathematics, 1997 A new kind of weighted graphs is studied when the weights of the edges belong to a partially ordered set \(L\). For such \(L\), the weight of a path is equal to the product of the weights of its edges. The distance between two vertices is defined as the lower bound of the weights of all paths joining those two vertices.
Alpin J., Mubarakzianow R.
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Weighted Modulo Orientations of Graphs and Signed Graphs
The Electronic Journal of Combinatorics, 2022 Given a graph $G$ and an odd prime $p$, for a mapping $f: E(G) \to {\mathbb Z}_p\setminus\{0\}$ and a ${\mathbb Z}_p$-boundary $b$ of $G$, an orientation $\tau$ is called an $(f,b;p)$-orientation if the net out $f$-flow is the same as $b(v)$ in ${\mathbb Z}_p$ at each vertex $v\in V(G)$ under orientation $D$.
Jianbing Liu +2 more
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ionicf/graph-make-undirected: Convert a directed graph to an undirected graph
, 2023 <p>Convert a directed graph to an undirected graph.</p> <pre><code># Convert the web-Stanford directed graph to an undirected graph.
Subhajit Sahu
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Finite Asymptotic Clusters of Metric Spaces
Theory and Applications of Graphs, 2018 Let $(X, d)$ be an unbounded metric space and let $\tilde r=(r_n)_{n\in\mathbb N}$ be a sequence of positive real numbers tending to infinity. A pretangent space $\Omega_{\infty, \tilde r}^{X}$ to $(X, d)$ at infinity is a limit of the rescaling sequence
Viktoriia Bilet, Oleksiy Dovgoshey
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Journal of Graph Theory, 2008 Abstract Suppose the edges of a graph G are assigned 3‐element lists of real weights. Is it possible to choose a weight for each edge from its list so that the sums of weights around adjacent vertices were different?
Tomasz Bartnicki +2 more
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Packing Triangles in Weighted Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2014 Tuza conjectured that for every graph $G$ the maximum size $\nu$ of a set of edge-disjoint triangles and minimum size $\tau$ of a set of edges meeting all triangles satisfy $\tau \leq 2\nu$. We consider an edge-weighted version of this conjecture, which amounts to packing and covering triangles in multigraphs.
Chapuy, Guillaume +4 more
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