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Research on Periodic Triangle Enumeration Algorithm for Temporal Graphs [PDF]
Jisuanji kexue yu tansuo, 2023 Real-world graphs are usually temporal graphs, and their edges are associated with timestamps. With the development of algorithms on graph data mining and the increase of needs in real-world, data mining algorithms for temporal graphs have started to ...
REN Zebin, LI Ronghua, DAI Yongheng, WANG Guoren
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On triangles in derangement graphs [PDF]
Journal of Combinatorial Theory, Series A, 2021 Given a permutation group $G$, the derangement graph $Γ_G$ of $G$ is the Cayley graph with connection set the set of all derangements of $G$. We prove that, when $G$ is transitive of degree at least $3$, $Γ_G$ contains a triangle. The motivation for this work is the question of how large can be the ratio of the independence number of $Γ_G$ to the size ...
Karen Meagher +2 more
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THE (△,□)-EDGE GRAPH G△,□ OF A GRAPH G [PDF]
Journal of Algebraic Systems, 2020 To a simple graph $G=(V,E)$, we correspond a simple graph $G_{\triangle,\square}$ whose vertex set is $\{\{x,y\}: x,y\in V\}$ and two vertices $\{x,y\},\{z,w\}\in G_{\triangle,\square}$ are adjacent if and only if $\{x,z\},\{x,w\},\{y,z\},\{y,w\}\in V ...
Gh. A. Nasiriboroujeni +2 more
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Triangle‐free equimatchable graphs [PDF]
Journal of Graph Theory, 2021 AbstractA graph is called equimatchable if all of its maximal matchings have the same size. Frendrup et al. provided a characterization of equimatchable graphs with girth at least 5. In this paper, we extend this result by providing a complete structural characterization of equimatchable graphs with girth at least 4, that is, equimatchable graphs with ...
Yasemin Büyükçolak +2 more
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Eigenvalues and triangles in graphs [PDF]
Combinatorics, Probability and Computing, 2020 AbstractBollobás and Nikiforov (J. Combin. Theory Ser. B.97 (2007) 859–865) conjectured the following. If G is a Kr+1-free graph on at least r+1 vertices and m edges, then ${\rm{\lambda }}_1^2(G) + {\rm{\lambda }}_2^2(G) \le (r - 1)/r \cdot 2m$, where λ1 (G)and λ2 (G) are the largest and the second largest eigenvalues of the adjacency matrix A(G ...
Huiqiu Lin +2 more
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Random Cyclic Triangle-Free Graphs of Prime Order
Journal of Mathematics, 2021 Cyclic triangle-free process (CTFP) is the cyclic analog of the triangle-free process. It begins with an empty graph of order n and generates a cyclic graph of order n by iteratively adding parameters, chosen uniformly at random, subject to the ...
Yu Jiang +3 more
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Nowhere-Zero Unoriented 6-Flows on Certain Triangular Graphs
Discussiones Mathematicae Graph Theory, 2022 A nowhere-zero unoriented flow of graph G is an assignment of non-zero real numbers to the edges of G such that the sum of the values of all edges incident with each vertex is zero. Let k be a natural number.
Yang Fan, Li Liangchen, Zhou Sizhong
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A Triangle Process on Regular Graphs [PDF]
, 2021 Switches are operations which make local changes to the edges of a graph, usually with the aim of preserving the vertex degrees. We study a restricted set of switches, called triangle switches. Each triangle switch creates or deletes at least one triangle.
Cooper, C, Dyer, M, Greenhill, C
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The Edge-To-Vertex Triangle Free Detor Distance in Graphs
Ratio Mathematica, 2022 For every connected graph G, the triangle free detour distance D∆f(u, v) is the length of a longest u- v triangle free path in G, where u, v are the vertices of G. A u-v triangle free path of length D∆f(u, v) is called the u-v triangle free detour.
S Lourdu Elqueen, G Priscilla Pacifica
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Bounds for the augmented Zagreb index
Theory and Applications of Graphs, 2023 The augmented Zagreb index (\rm{AZI} for short) of a graph $G$, introduced by Furtula et al. in 2010, is defined as ${\rm AZI}(G)=\sum\limits_{v_iv_j\in E(G)}{\left(\frac{d(v_i)d(v_j)}{d(v_i)+d(v_j)-2}\right)}^3$, where $E(G)$ is the edge set of $G$, and
Ren qingcuo +3 more
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