Results 11 to 20 of about 149 (128)
On the planarity of line Mycielskian graph of a graph [PDF]
Ratio Mathematica, 2020 The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤ i ≤ q and e, then for 1 ≤ i ≤ q , joining ei' to the neighbours of ei and to e.
Keerthi G. Mirajkar +1 more
doaj +2 more sources
Hypermaps Over Non-Abelian Simple Groups and Strongly Symmetric Generating Sets [PDF]
, 2023 A generating pair x, y for a group G is said to be symmetric if there exists an automorphism φx,y of G inverting both x and y, that is, xφx,y = x−1 and yφx,y = y−1.
Spiga P., Lucchini A.
core +1 more source
Large expanders in high genus unicellular maps [PDF]
, 2022 We study large uniform random maps with one face whose genus grows linearly with the number of edges. They can be seen as a model of discrete hyperbolic geometry.
Louf, Baptiste
core +1 more source
, 2021 In this paper we define a way to get a bounded invertible automaton starting from a finite graph. It turns out that the corresponding automaton group is regular weakly branch over its commutator subgroup, contains a free semigroup on two elements and is ...
Donno A. +3 more
core +1 more source
Classes of graphs embeddable in order-dependent surfaces [PDF]
, 2023 Given a function \(g=g(n)\) we let \(\mathcal{E}^g\) be the class of all graphs \(G\) such that if \(G\) has order \(n\) (that is, has \(n\) vertices) then it is embeddable in some surface of Euler genus at most \(g(n)\), and let \(\widetilde{\mathcal E}^
McDiarmid, Colin, Saller, Sophia
core +1 more source
Discussiones Mathematicae Graph Theory, 2023 DP-coloring is generalized via relaxed coloring and variable degeneracy in [P. Sittitrai and K. Nakprasit, Su cient conditions on planar graphs to have a relaxed DP-3-coloring, Graphs Combin. 35 (2019) 837–845], [K.M. Nakprasit and K.
Sribunhung Sarawute +3 more
doaj +1 more source
Regularity and Planarity of Token Graphs
Discussiones Mathematicae Graph Theory, 2017 Let G = (V, E) be a graph of order n and let 1 ≤ k < n be an integer. The k-token graph of G is the graph whose vertices are all the k-subsets of V, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G.
Carballosa Walter +3 more
doaj +1 more source
Additive List Coloring of Planar Graphs with Given Girth
Discussiones Mathematicae Graph Theory, 2020 An additive coloring of a graph G is a labeling of the vertices of G from {1, 2, . . . , k} such that two adjacent vertices have distinct sums of labels on their neighbors.
Brandt Axel +2 more
doaj +1 more source
The Planar Index and Outerplanar Index of Some Graphs Associated to Commutative Rings
Discussiones Mathematicae - General Algebra and Applications, 2019 In this paper, we study the planar and outerplanar indices of some graphs associated to a commutative ring. We give a full characterization of these graphs with respect to their planar and outerplanar indices when R is a finite ring.
Barati Zahra, Afkhami Mojgan
doaj +1 more source
Non-1-Planarity of Lexicographic Products of Graphs
Discussiones Mathematicae Graph Theory, 2021 In this paper, we show the non-1-planarity of the lexicographic product of a theta graph and K2. This result completes the proof of the conjecture that a graph G ◦ K2 is 1-planar if and only if G has no edge belonging to two cycles.
Matsumoto Naoki, Suzuki Yusuke
doaj +1 more source