Results 11 to 20 of about 14,956 (263)
Secure monophonic domination of graphs [PDF]
Journal of HyperstructuresLet G = (V, E) be a connected graph. A monophonic dominating set M is said to be a secure monophonic dominating set Sm (abbreviated as SMD set) of G if for each v∈V \M there exists u∈M such that v is adjacent to u and Sm = {M \(u)} ∪{v} is a monophonic ...
K Sunitha, D Divya
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Multiple Petersen Subdivisions in Permutation Graphs [PDF]
The Electronic Journal of Combinatorics, 2013 A permutation graph is a cubic graph admitting a 1-factor $M$ whose complement consists of two chordless cycles. Extending results of Ellingham and of Goldwasser and Zhang, we prove that if $e$ is an edge of $M$ such that every 4-cycle containing an edge of $M$ contains $e$, then $e$ is contained in a subdivision of the Petersen graph of a special type.
Kaiser, Tomáš +2 more
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IEEE Access, 2018 The resistance distance is widely used in random walk, electronic engineering, and complex networks. One of the main topics in the study of the resistance distance is the computation problem.
Qun Liu, Jia-Bao Liu, Shaohui Wang
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Resolvability in Subdivision Graph of Circulant Graphs
Symmetry, 2023 Circulant networks are a very important and widely studied class of graphs due to their interesting and diverse applications in networking, facility location problems, and their symmetric properties. The structure of the graph ensures that it is symmetric about any line that cuts the graph into two equal parts.
Syed Ahtsham Ul Haq Bokhary +5 more
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First General Zagreb Co-Index of Graphs under Operations
Journal of Mathematics, 2022 Topological indices are graph-theoretic parameters which are widely used in the subject of chemistry and computer science to predict the various chemical and structural properties of the graphs respectively.
Muhammad Javaid +4 more
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Anagram-Free Colorings of Graph Subdivisions
SIAM Journal on Discrete Mathematics, 2018 An anagram is a word of the form $WP$ where $W$ is a non-empty word and $P$ is a permutation of $W$. A vertex colouring of a graph is anagram-free if no subpath of the graph is an anagram. Anagram-free graph colouring was independently introduced by Kam ev, uczak and Sudakov and ourselves.
Tim E. Wilson, David R. Wood
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Odd K3,3 subdivisions in bipartite graphs
Journal of Combinatorial Theory, Series B, 2016 We prove that every internally 4-connected non-planar bipartite graph has an odd K_3,3 subdivision; that is, a subgraph obtained from K_3,3 by replacing its edges by internally disjoint odd paths with the same ends. The proof gives rise to a polynomial-time algorithm to find such a subdivision.
Thomas, Robin, Whalen, Peter
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Line and Subdivision Graphs Determined by T 4 -Gain Graphs [PDF]
Mathematics, 2019 Let T 4 = { ± 1 , ± i } be the subgroup of fourth roots of unity inside T , the multiplicative group of complex units. For a T 4 -gain graph Φ = ( Γ , T 4 , φ ) , we introduce gain functions on its line graph L ( Γ ) and on its subdivision graph S ( Γ ) . The corresponding gain graphs L ( Φ ) and
Abdullah Alazemi +4 more
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Subdivisions in apex graphs [PDF]
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2012 The Kelmans-Seymour conjecture states that the 5-connected nonplanar graphs contain a subdivided $K_{_5}$. Certain questions of Mader propose a "plan" towards a possible resolution of this conjecture. One part of this plan is to show that a 5-connected nonplanar graph containing $K^-_{_4}$ or $K_{_{2,3}}$ as a subgraph has a subdivided $K_{_5 ...
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The nonsplit domination in subdivision graphs
Proyecciones (Antofagasta), 2020 A dominating set D of a graph G = (V, E) is a nonsplit dominating set if the induced subgraph 〈V − D〉 is connected. The nonsplit domination number γns(G) of G is the minimum cardinality of a nonsplit dominating set. An edge e = uv of a graph G is said to be subdivided if e is replaced by the edges uw and vw for some vertex w not in V (G).
R. Jemimal Chrislight +1 more
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