Results 31 to 40 of about 937,585 (316)
Mixed Graph Colorings: A Historical Review
Mathematics, 2020 This paper presents a historical review and recent developments in mixed graph colorings in the light of scheduling problems with the makespan criterion. A mixed graph contains both a set of arcs and a set of edges. Two types of colorings of the vertices
Yuri N. Sotskov
doaj +1 more source
Graphs with mixed metric dimension three and related algorithms
AIMS Mathematics, 2023 Let $ G = (V, E) $ be a simple connected graph. A vertex $ x\in V(G) $ resolves the elements $ u, v\in E(G)\cup V(G) $ if $ d_G(x, u)\neq d_G(x, v) $.
Dalal Awadh Alrowaili +3 more
doaj +1 more source
HS-integral and Eisenstein integral mixed circulant graphs
Theory and Applications of Graphs, 2023 A mixed graph is called \emph{second kind hermitian integral} (\emph{HS-integral}) if the eigenvalues of its Hermitian-adjacency matrix of the second kind are integers.
Monu Kadyan, Bikash Bhattacharjya
doaj +1 more source
Discrete Mathematics & Theoretical Computer Science, 2023 Mixed graphs have both directed and undirected edges. A mixed cage is a regular mixed graph of given girth with minimum possible order. In this paper mixed cages are studied. Upper bounds are obtained by general construction methods and computer searches.
Geoffrey Exoo
doaj +1 more source
Mixed graph edge coloring [PDF]
Discrete Mathematics, 2009 AbstractWe are interested in coloring the edges of a mixed graph, i.e., a graph containing unoriented and oriented edges. This problem is related to a communication problem in job-shop scheduling systems. In this paper we give general bounds on the number of required colors and analyze the complexity status of this problem. In particular, we provide NP-
Furmańczyk, Hanna +3 more
openaire +3 more sources
A family of mixed graphs with large order and diameter 2 [PDF]
, 2017 A mixed regular graph is a connected simple graph in which each vertex has both a fixed outdegree (the same indegree) and a fixed undirected degree.
Araujo Pardo, Gabriela +3 more
core +2 more sources
Discrete Applied Mathematics, 2017 A mixed graph can be seen as a type of digraph containing some edges (two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and iterated line digraphs. These structures are proven to be useful in the problem of constructing dense graphs or digraphs, and this is related to the ...
Dalfó Simó, Cristina +2 more
openaire +6 more sources
MixedGraphinFuzzy,Neutrosophic, and Plithogenic Graphs [PDF]
Neutrosophic Sets and SystemsGraph theory examines networks consisting of nodes (vertices) and the connections (edges) between them. Mixed graphs, which combine both undirected and directed edges, provide a versatile framework for representing relationships with symmetric and ...
Florentin Smarandache, Takaaki Fujita
doaj +1 more source
Computing the Mixed Metric Dimension of a Generalized Petersen Graph P(n, 2)
Frontiers in Physics, 2020 Let Γ = (V, E) be a connected graph. A vertex i ∈ V recognizes two elements (vertices or edges) j, k ∈ E ∩ V, if dΓ(i, j) ≠ dΓ(i, k). A set S of vertices in a connected graph Γ is a mixed metric generator for Γ if every two distinct elements (vertices or
Hassan Raza, Ying Ji
doaj +1 more source
$\mathcal{B}$-Partitions, determinant and permanent of graphs [PDF]
Transactions on Combinatorics, 2018 Let $G$ be a graph (directed or undirected) having $k$ number of blocks $B_1, B_2,\hdots,B_k$. A $\mathcal{B}$-partition of $G$ is a partition consists of $k$ vertex-disjoint subgraph $(\hat{B_1},\hat{B_1},\hdots,\hat{B_k})$ such that $\hat{B}_i$ is an ...
Ranveer Singh, Ravindra Bapat
doaj +1 more source