Results 41 to 50 of about 163 (126)
Minimally Strong Subgraph (k,ℓ)-Arc-Connected Digraphs
Discussiones Mathematicae Graph Theory, 2022 Let D = (V,A) be a digraph of order n, S a subset of V of size k and 2 ≤ k ≤ n. A subdigraph H of D is called an S-strong subgraph if H is strong and S ⊆ V (H). Two S-strong subgraphs D1 and D2 are said to be arc-disjoint if A(D1) ∩ A(D2) = ∅.
Sun Yuefang, Jin Zemin
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On the Metric Dimension of Directed and Undirected Circulant Graphs
Discussiones Mathematicae Graph Theory, 2020 The undirected circulant graph Cn(±1, ±2, . . . , ±t) consists of vertices v0, v1, . . . , vn−1 and undirected edges vivi+j, where 0 ≤ i ≤ n − 1, 1 ≤ j ≤ t (2 ≤ t ≤ n2{n \over 2} ), and the directed circulant graph Cn(1, t) consists of vertices v0, v1, .
Vetrík Tomáš
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Maximal Independent Sets In Graphs With At Most r Cycles
, 2005 Key Words: cycle, ear decomposition, maximal independent set AMS classification: Primary 05C35; Secondary 05C38, 05C69. We find the maximum number of maximal independent sets in two families of graphs.
Vincent R. Vatter +11 more
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Contraharmonic Index: Extremal Results for Unicyclic Graphs and Bounds for General Graphs
Journal of Mathematics, Volume 2026, Issue 1, 2026.Let G be a graph with edge set E(G). The degree of a vertex w in G is denoted by dw. The contraharmonic index of G is defined as CHG=∑uv∈EGdu+dv−1du2+dv2. In this paper, we investigate several properties of the contraharmonic index, including extremal results for unicyclic graphs of a given order, as well as bounds and the effects of an edge removal in
Abdulaziz Mutlaq Alotaibi +2 more
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A Sharp Upper Bound on Algebraic Connectivity Using Domination Number [PDF]
, 2020 Let G be a connected graph of order n. The algebraic connectivity of G is the second smallest eigenvalue of the Laplacian matrix of G. A dominating set in G is a vertex subset S such that each vertex of G that is not in S is adjacent to a vertex in S ...
D Stevanović, P Hansen, M Aouchiche
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On General Sum‐Connectivity Index and Number of Segments of Fixed‐Order Chemical Trees
Journal of Mathematics, Volume 2025, Issue 1, 2025.Nowadays, one of the most active areas in mathematical chemistry is the study of the mathematical characteristics associated with molecular descriptors. The primary objective of the current study is to find the largest value of χα of graphs in the class of all fixed‐order chemical trees with a particular number of segments for α > 1, where χα is the ...
Muzamil Hanif +5 more
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The Binding Number of a Zero Divisor Graph [PDF]
, 2013 In this paper, we evaluate b(Γ(Z n )). Our main result is, we give maximum value of b(Γ(Z n )) is 0.99999999796427626489236243072661, where n is any positive integer upto fiftieth million.
J Ravi Sankar +3 more
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Detour index of a class of unicyclic graphs
, 2010 The detour index of a connected graph is defined as the sum of detour distances between all unordered pairs of vertices. We determine the n-vertex unicyclic graphs whose vertices on its unique cycle all have degree at least three with the first, the ...
Qi Xuli, Bo Zhou
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Journal of Mathematics, Volume 2025, Issue 1, 2025.In its crystalline state, the α‐icosahedral nanosheet of boron demonstrates superconductivity and thermal electronic properties. Mathematical research on a graph’s structure yields a graph descriptor, a numerical measure. Chemical graph theory employs connectivity descriptors to analyze molecular structures, providing crucial insights into many ...
Khalil Hadi Hakami +3 more
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Gaps in the Saturation Spectrum of Trees
Discussiones Mathematicae Graph Theory, 2019 A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from the complement of G to G results in a copy of H. The minimum number of edges (the size) of an H-saturated graph on n vertices is denoted sat(n,H), while the maximum ...
Horn Paul +3 more
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