Results 21 to 30 of about 6,109 (206)
Non-Bipartite K-Common Graphs [PDF]
Combinatorica, 2022 A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of K_n is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, Stovicek and Thomason [Combinatorica 16 (1996), 123-141]. We also show that a graph H is k-common for
Králʼ, Daniel +4 more
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Bounds for the Kirchhoff Index of Bipartite Graphs
Journal of Applied Mathematics, 2012 A -bipartite graph is a bipartite graph such that one bipartition has m vertices and the other bipartition has n vertices. The tree dumbbell consists of the path together with a independent vertices adjacent to one pendent vertex of and b independent ...
Yujun Yang
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Inverses of Bipartite Graphs [PDF]
Combinatorica, 2017 Let $G$ be a bipartite graph and its adjacency matrix $\mathbb A$. If $G$ has a unique perfect matching, then $\mathbb A$ has an inverse $\mathbb A^{-1}$ which is a symmetric integral matrix, and hence the adjacency matrix of a multigraph. The inverses of bipartite graphs with unique perfect matchings have a strong connection to M bius functions of ...
Yang, Yujun, Ye, Dong
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Role coloring bipartite graphs
Discrete Applied Mathematics, 2022 A k-role coloring of a graph G is an assignment of k colors to the vertices of G such that if any two vertices are assigned the same color, then their neighborhood are assigned the same set of colors. By definition, every graph on n vertices admits an n-role coloring.
Sukanya Pandey, Vibha Sahlot
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Advances in Materials Science and Engineering, 2023 The application of bipartite and regular graphs plays a vital role in the area of engineering, mathematical sciences, design of experiments, and medical fields.
P. Karthikeyan +4 more
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International Journal of Computer Mathematics: Computer Systems Theory, 2020 Given a bipartite graph G = ( X , Y , E ) , the bipartite dot product representation of G is a function f : X ∪ Y → R k and a positive threshold t such that for any x ∈ X and y ∈ Y , x y ∈ E if and...
Bailey, Sean, Brown, David E.
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Algorithmic Aspects of Secure Connected Domination in Graphs
Discussiones Mathematicae Graph Theory, 2021 Let G = (V, E) be a simple, undirected and connected graph. A connected dominating set S ⊆ V is a secure connected dominating set of G, if for each u ∈ V \ S, there exists v ∈ S such that (u, v) ∈ E and the set (S \ {v}) ∪ {u} is a connected dominating ...
Kumar Jakkepalli Pavan +1 more
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Mathematics, 2021 In recent decades, distributed consensus-based algorithms for data aggregation have been gaining in importance in wireless sensor networks since their implementation as a complementary mechanism can ensure sensor-measured values with high reliability and
Martin Kenyeres, Jozef Kenyeres
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Edge-Coloring Bipartite Graphs [PDF]
Journal of Algorithms, 2000 This note provides an algorithm for finding \(\Delta\)(colors)-edge-coloring of a bipartite graph of order \(n\) and size \(m\) in time \(T+O(m\log \Delta)\) where \(T\) is the time needed to find a perfect matching in a \(k\)-regular bipartite graph, \(k\leq \Delta\), and \(\Delta\) is the maximum degree of vertices.
A. Kapoor, Rizzi, Romeo
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Homomorphisms of infinite bipartite graphs onto complete bipartite graphs [PDF]
Czechoslovak Mathematical Journal, 1983 Let B be a bipartite graph on the vertex sets C, D. A homomorphism \(\phi\) of B onto a complete bipartite graph \(K_{r,s}\) is said to be bicomplete if \(\phi(x)=\phi(y)\) only if either both x, y belong to C, or both x, y belong to D. For a connected bipartite graph B, the author defines the parameter \(\beta_ 0(B)\) as the supremum of all values of ...
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