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Confluence theory for graphs [PDF]
Algebraic & Geometric Topology, 2007 We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie algebra of rank at most 2, gives rise to a confluent system of reduction rules of graphs (via Kuperberg's spiders ...
Sikora, Adam, Westbury, Bruce
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Further results on local inclusive distance vertex irregularity strength of graphs
Electronic Journal of Graph Theory and Applications, 2023 Let G = (V, E) be a simple undirected graph. A labeling f : V(G)→{1, …, k} is a local inclusive d-distance vertex irregular labeling of G if every adjacent vertices x, y ∈ V(G) have distinct weights, with the weight w(x),x ∈ V(G) is the sum of every ...
Fawwaz Fakhrurrozi Hadiputra +3 more
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Graceful labeling construction for some special tree graph using adjacency matrix
Electronic Journal of Graph Theory and Applications, 2023 In 1967, Rosa introduced β − labeling which was then popularized by Golomb under the name graceful. Graceful labeling on a graph G is an injective function f : V(G)→{0, 1, 2, …, |E(G)|} such that, when each edge uv ∈ E(G) is assigned the label |f(u)−f(v)|
Nikson Simarmata +2 more
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The total vertex irregularity strength of symmetric cubic graphs of the Foster's Census
Indonesian Journal of Combinatorics, 2022 Foster (1932) performed a mathematical census for all connected symmetric cubic (trivalent) graphs of order n with n ≤ 512. This census then was continued by Conder et al. (2006) and they obtained the complete list of all connected symmetric cubic graphs
Rika Yanti +3 more
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On the strong beta-number of galaxies with three and four components
AKCE International Journal of Graphs and Combinatorics, 2020 The beta-number of a graph is the smallest positive integer for which there exists an injective function such that each is labeled and the resulting set of edge labels is for some positive integer . The beta-number of is if there exists no such integer .
Rikio Ichishima +2 more
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The consecutively super edge-magic deficiency of graphs and related concepts
Electronic Journal of Graph Theory and Applications, 2020 A bipartite graph G with partite sets X and Y is called consecutively super edge-magic if there exists a bijective function f : V(G) ⋃ E(G) → {1,2,...,|V(G)| + |E(G)|} with the property that f(X) = {1,2,...,|X|}, f(Y) = {|X|+1, |X|+2,...,|V(G)|} and f(u)+
Rikio Ichishima +2 more
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AKCE International Journal of Graphs and Combinatorics, 2020 Let be a graph of order . A numbering of is a labeling that assigns distinct elements of the set to the vertices of , where each edge of is labeled .
Rikio Ichishima +2 more
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On the beta-number of linear forests with an even number of components
AKCE International Journal of Graphs and Combinatorics, 2018 The beta-number of a graph is the smallest positive integer for which there exists an injective function such that each is labeled and the resulting set of edge labels is for some positive integer . The beta-number of is , otherwise.
Rikio Ichishima, Akito Oshima
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Symmetry, 2018 This book contains the successful invited submissions [1–10] to a special issue of Symmetry on the subject area of ‘graph theory’ [...]
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CoRR, 2015 This book is based on Graph Theory courses taught by P.A. Petrosyan, V.V. Mkrtchyan and R.R. Kamalian at Yerevan State University.
Petros A. Petrosyan +2 more
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