Results 11 to 20 of about 6,426 (117)
From light edges to strong edge-colouring of 1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 A strong edge-colouring of an undirected graph $G$ is an edge-colouring where every two edges at distance at most~$2$ receive distinct colours. The strong chromatic index of $G$ is the least number of colours in a strong edge-colouring of $G$.
Julien Bensmail +3 more
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Combinatorial optimization in networks with Shared Risk Link Groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 The notion of Shared Risk Link Groups (SRLG) captures survivability issues when a set of links of a network may fail simultaneously. The theory of survivable network design relies on basic combinatorial objects that are rather easy to compute in the ...
David Coudert +3 more
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On Proper (Strong) Rainbow Connection of Graphs
Discussiones Mathematicae Graph Theory, 2021 A path in an edge-colored graph G is called a rainbow path if no two edges on the path have the same color. The graph G is called rainbow connected if between every pair of distinct vertices of G, there is a rainbow path.
Jiang Hui +3 more
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General Randic matrix and general Randi'c energy [PDF]
Transactions on Combinatorics, 2014 Let $G$ be a simple graph with vertex set $V(G) = {v_1, v_2,ldots , v_n}$ and $d_i$ the degree of its vertex $v_i$, $i = 1, 2, cdots, n$. Inspired by the Randi'c matrix and the general Randi'c index of a graph, we introduce the concept of general ...
Ran Gu;, Fei Huang, Xueliang Li
doaj
Rainbow Vertex-Connection and Forbidden Subgraphs
Discussiones Mathematicae Graph Theory, 2018 A path in a vertex-colored graph is called vertex-rainbow if its internal vertices have pairwise distinct colors. A vertex-colored graph G is rainbow vertex-connected if for any two distinct vertices of G, there is a vertex-rainbow path connecting them ...
Li Wenjing, Li Xueliang, Zhang Jingshu
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On interval number in cycle convexity [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 Recently, Araujo et al. [Manuscript in preparation, 2017] introduced the notion of Cycle Convexity of graphs. In their seminal work, they studied the graph convexity parameter called hull number for this new graph convexity they proposed, and they ...
Julio Araujo +3 more
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Odd Harmonious Labeling of Pn ⊵ C4 and Pn ⊵ D2(C4)
Indonesian Journal of Combinatorics, 2021 A graph G with q edges is said to be odd harmonious if there exists an injection f:V(G) → ℤ2q so that the induced function f*:E(G)→ {1,3,...,2q-1} defined by f*(uv)=f(u)+f(v) is a bijection.Here we show that graphs constructed by edge comb product of ...
Sabrina Shena Sarasvati +2 more
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Erdős-Gallai-Type Results for Total Monochromatic Connection of Graphs
Discussiones Mathematicae Graph Theory, 2019 A graph is said to be total-colored if all the edges and the vertices of the graph are colored. A total-coloring of a graph is a total monochromatically-connecting coloring (TMC-coloring, for short) if any two vertices of the graph are connected by a ...
Jiang Hui, Li Xueliang, Zhang Yingying
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Skew Randi'c matrix and skew Randi'c energy [PDF]
Transactions on Combinatorics, 2016 Let $G$ be a simple graph with an orientation $sigma$, which assigns to each edge a direction so that $G^sigma$ becomes a directed graph. $G$ is said to be the underlying graph of the directed graph $G^sigma$.
Ran Gu, Fei Huang, Xueliang Li
doaj
Backbone colouring and algorithms for TDMA scheduling [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 We investigate graph colouring models for the purpose of optimizing TDMA link scheduling in Wireless Networks. Inspired by the BPRN-colouring model recently introduced by Rocha and Sasaki, we introduce a new colouring model, namely the BMRN-colouring ...
Julien Bensmail +4 more
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