Results 41 to 50 of about 100,234 (286)
Vertex-Transitive Direct Products of Graphs
The Electronic Journal of Combinatorics, 2018 It is known that for graphs $A$ and $B$ with odd cycles, the direct product $A\times B$ is vertex-transitive if and only if both $A$ and $B$ are vertex-transitive. But this is not necessarily true if one of $A$ or $B$ is bipartite, and until now there has been no characterization of such vertex-transitive direct products.
Richard H. Hammack, Wilfried Imrich
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Total colouring of some cartesian and direct product graphs
, 2020 A graph is $k$-total colourable if there is an assignment of $k$ different colours to the vertices and edges of the graph such that no two adjacent nor incident elements receive the same colour.
MacKeigan, Kyle, Janssen, Jeannette
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Injective coloring of product graphs
, 2023 The problem of injective coloring in graphs can be revisited through two different approaches: coloring the two-step graphs and vertex partitioning of graphs into open packing sets, each of which is equivalent to the injective coloring problem itself ...
Samadi, Babak +3 more
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Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2007 In this paper we study the graphs which are direct product of a simple graph G with the graphs obtained by the complete graph Kk adding a loop to each vertex; thus these graphs turn out to be a generalization of the double graphs.
Zagaglia Salvi, Norma +1 more
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Generalized Petersen graphs and Kronecker covers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 The family of generalized Petersen graphs $G(n,k)$, introduced by Coxeter et al. [4] and named by Mark Watkins (1969), is a family of cubic graphs formed by connecting the vertices of a regular polygon to the corresponding vertices of a star polygon. The
Matjaž Krnc, Tomaž Pisanski
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The irregularity of graphs under graph operations
Discussiones Mathematicae Graph Theory, 2014 The irregularity of a simple undirected graph G was defined by Albertson [5] as irr(G) = ∑uv∈E(G) |dG(u) − dG(v)|, where dG(u) denotes the degree of a vertex u ∈ V (G).
Abdo Hosam, Dimitrov Darko
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On global (strong) defensive alliances in some product graphs
Communications in Combinatorics and Optimization, 2017 A defensive alliance in a graph is a set $S$ of vertices with the property that every vertex in $S$ has at most one more neighbor outside of $S$ than it has inside of $S$. A defensive alliance $S$ is called global if it forms a dominating set. The
Ismael Gonz\'alez Yero +2 more
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On Certain Products of Complex Intuitionistic Fuzzy Graphs
Journal of Function Spaces, 2021 A complex intuitionistic fuzzy set (CIFS) can be used to model problems that have both intuitionistic uncertainty and periodicity. A diagram composed of nodes connected by lines and labeled with specific information may be used to depict a wide range of ...
Abida Anwar, Faryal Chaudhry
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Enumerating cliques in direct product graphs [PDF]
Journal of Combinatorics, 2020 5 pages, 1 ...
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The general position problem and strong resolving graphs
Open Mathematics, 2019 The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three pairwise distinct vertices from S lie on a common geodesic.
Klavžar Sandi, Yero Ismael G.
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