Results 21 to 30 of about 445 (76)
The H-force sets of the graphs satisfying the condition of Ore’s theorem
Open Mathematics, 2020 Let G be a Hamiltonian graph. A nonempty vertex set X⊆V(G)X\subseteq V(G) is called a Hamiltonian cycle enforcing set (in short, an H-force set) of G if every X-cycle of G (i.e., a cycle of G containing all vertices of X) is a Hamiltonian cycle.
Zhang Xinhong, Li Ruijuan
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Equating κ Maximum Degrees in Graphs without Short Cycles
Discussiones Mathematicae Graph Theory, 2020 For an integer k at least 2, and a graph G, let fk(G) be the minimum cardinality of a set X of vertices of G such that G − X has either k vertices of maximum degree or order less than k.
Fürst Maximilian +4 more
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More on Comparison Between First Geometric-Arithmetic Index and Atom-Bond Connectivity Index [PDF]
, 2015 The first geometric-arithmetic (GA) index and atom-bond connectivity (ABC) index are molecular structure descriptors which play a significant role in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship ...
Akbar Ali +3 more
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The Second Neighbourhood for Bipartite Tournaments
Discussiones Mathematicae Graph Theory, 2019 Let T (X ∪ Y, A) be a bipartite tournament with partite sets X, Y and arc set A. For any vertex x ∈ X ∪Y, the second out-neighbourhood N++(x) of x is the set of all vertices with distance 2 from x.
Li Ruijuan, Sheng Bin
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Eccentric topological properties of a graph associated to a finite dimensional vector space
Main Group Metal Chemistry, 2020 A topological index is actually designed by transforming a chemical structure into a number. Topological index is a graph invariant which characterizes the topology of the graph and remains invariant under graph automorphism.
Liu Jia-Bao +5 more
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On Implicit Heavy Subgraphs and Hamiltonicity of 2-Connected Graphs
Discussiones Mathematicae Graph Theory, 2021 A graph G of order n is implicit claw-heavy if in every induced copy of K1,3 in G there are two non-adjacent vertices with sum of their implicit degrees at least n. We study various implicit degree conditions (including, but not limiting to, Ore- and Fan-
Zheng Wei, Wideł Wojciech, Wang Ligong
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, 2015 A \textit{primitive hole} of a graph $G$ is a cycle of length $3$ in $G$. The number of primitive holes in a given graph $G$ is called the primitive hole number of that graph $G$. The primitive degree of a vertex $v$ of a given graph $G$ is the number of
C. Susanth +4 more
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Non-commuting graph of the dihedral group determined by Hosoya parameters
Alexandria Engineering Journal, 2022 Hosoya introduced the concept of graph terminologies in chemistry and provide a modeling for molecules. This modeling leads to predict the chemical properties of molecules, easy classification of chemical compounds, computer simulations and computer ...
Muhammad Salman +4 more
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On Order Prime Divisor Graphs of Finite Groups
Discussiones Mathematicae - General Algebra and Applications, 2021 The order prime divisor graph 𝒫𝒟(G) of a finite group G is a simple graph whose vertex set is G and two vertices a, b ∈ G are adjacent if and only if either ab = e or o(ab) is some prime number, where e is the identity element of the group G and o(x ...
Sen Mridul K. +2 more
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Discrete Mathematics & Theoretical Computer Science, 2018 We define a weakly threshold sequence to be a degree sequence $d=(d_1,\dots,d_n)$ of a graph having the property that $\sum_{i \leq k} d_i \geq k(k-1)+\sum_{i > k} \min\{k,d_i\} - 1$ for all positive $k \leq \max\{i:d_i \geq i-1\}$.
Michael D. Barrus
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