Results 61 to 70 of about 580,793 (206)
Inequalities for Distance Signless Laplacian Matrix Under Minimum‐Degree Constraints
Journal of Mathematics, Volume 2026, Issue 1, 2026.For a connected graph G of order n, let D(G) denote its distance matrix and let Tr(G) be the diagonal matrix formed by the vertex transmissions. The distance signless Laplacian of G is defined by DQ = D(G) + Tr(G). The largest eigenvalue of DQ, written as ∂1QG, is referred to as the distance signless Laplacian spectral radius of G.
Mohd Abrar Ul Haq +3 more
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The k-Metric Dimension of a Unicyclic Graph
, 2021 Given a connected graph G=(V(G),E(G)), a set S⊆V(G) is said to be a k-metric generator for G if any pair of different vertices in V(G) is distinguished by at least k elements of S.
Alejandro Estrada-Moreno
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Maximum Reciprocal Degree Resistance Distance Index of Unicyclic Graphs
Discrete Dynamics in Nature and Society, 2020 The reciprocal degree resistance distance index of a connected graph G is defined as RDRG=∑u,v⊆VGdGu+dGv/rGu,v, where rGu,v is the resistance distance between vertices u and v in G. Let Un denote the set of unicyclic graphs with n vertices.
Gai-Xiang Cai, Xing-Xing Li, Gui-Dong Yu
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Maximum Value of the ABC Index of the Edge‐Corona Graph of Two Graphs
Journal of Mathematics, Volume 2026, Issue 1, 2026.This paper is concerned with the atom‐bond connectivity index (ABC index), defined as ABCG=∑uv∈EGdu+dv−2/dudv, where E(G) is the edge set of G and du and dv are degrees of vertices u and v, respectively. G1□G2 denotes the edge‐corona graph of G1 and G2.
Haiqin Liu, Yanling Shao, Pramita Mishra
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The largest eigenvalue of unicyclic graphs
Discrete Mathematics, 2007 The author shows that the largest eigenvalue of the adjacency matrix of a unicyclic graph with the maximum vertex degree \(\Delta\) is bounded from above by \(2\sqrt{\Delta-1}\), while the largest eigenvalue of its Laplacian matrix is bounded by \(\Delta+2\sqrt{\Delta-1}\), with equality in the first case holding for all cycles, and in the second case ...
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, 2020 {"references": ["1.\tJ. Amalorpava Jerline, L. Benedict Michaelraj, On a conjecture of harmonic index and diameter of graphs, Kragujevac Journal of Mathematics, 40(1), (2016),73-78. 2.\tR. Balakrishnan, K. Ranganathan, A Textbook of Graph Theory, Springer-Verlog, New York, 2000. 3.\tH. Deng, S. Balachandran, S. K. Ayyaswamy, Y. B.
I. Ignomary, S. Suganya
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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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AN ISOMORPHISM THEOREM FOR UNICYCLIC GRAPHS
Demonstratio Mathematica, 1993 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A New Kind of Dominated Coloring of Some Special Graphs
Journal of Mathematics, Volume 2026, Issue 1, 2026.This paper introduces the concept of locating‐dominated coloring, a new graph coloring parameter that merges the properties of dominated coloring and locating coloring. For a connected graph G, a locating‐dominated coloring is defined as a proper dominated k‐coloring of G using an ordered partition of V(G) to k‐color classes Π = (C1, C2, …, Ck) such ...
F. Poryousefi +3 more
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Fast Construction on a Restricted Budget
Random Structures &Algorithms, Volume 67, Issue 4, December 2025.ABSTRACT We introduce a model of a controlled random graph process. In this model, the edges of the complete graph Kn$$ {K}_n $$ are ordered randomly and then revealed, one by one, to a player called Builder. He must decide, immediately and irrevocably, whether to purchase each observed edge.
Alan Frieze +2 more
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