Results 61 to 70 of about 412,655 (203)
On the Absolute Sum of Chromatic Polynomial Coefficient of Graphs
International Journal of Mathematics and Mathematical Sciences, 2011 The absolute sum of chromatic polynomial coefficient of forest, q-tree, unicyclic graphs, and quasiwheel graphs, are determined in this paper.
Shubo Chen
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Bidegreed unicyclic graphs with minimum spectral radius
, 2013 In this paper we consider bidegreed graphs, namely graphs whose vertices have degree either Δ or δ, with Δ≠δ. In the latter setting we identify those unicyclic graphs minimizing the largest eigenvalue of the adjacency matrix.
LI MARZI, Enzo, BELARDO, FRANCESCO
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Ordering of minimal energies in unicyclic signed graphs [PDF]
, 2023 Let S = (G, σ) be a signed graph of order n and size m and let t1, t2, . . . , tn be the eigenvalues of S. The energy of S is defined as E(S) = Pnj=1|tj|. A connected signed graph is said to be unicyclic if its order and size are same.
Shamsher, Tahir +3 more
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New Sharp Extremal Bounds for the Randić Index of Trees With Prescribed Roman Domination Number
Discrete Dynamics in Nature and Society, Volume 2026, Issue 1, 2026.The Randić index is a classical degree‐based topological index that captures branching features of a graph and has broad applications in chemical graph theory and related network models. Roman domination is a defense‐inspired covering concept in which vertices are assigned protective labels so that every unprotected vertex is adjacent to a strongly ...
Waqar Ali +4 more
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Some Results on the Independence Polynomial of Unicyclic Graphs
Discussiones Mathematicae Graph Theory, 2018 Let G be a simple graph on n vertices. An independent set in a graph is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial I(G,x)=∑k=0ns(G,k)xk$I(G,x) = \sum\nolimits_{k = 0}^n {s\left({G,k} \right)x^k }$, where s(
Oboudi Mohammad Reza
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Trees With a Given Independence Number Maximizing the Randić Index
Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.The Randić index is a classical degree‐based descriptor with strong empirical connections to branching‐sensitive physicochemical properties of chemical compounds. Defined as R(G) = ∑uv ∈ E(G)1/√(d(u)d(v)), for a simple connected graph G, this index has been extensively studied, especially in the context of trees.
Bojana Borovićanin +3 more
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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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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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