Results 41 to 50 of about 314 (174)
On the nullity of unicyclic graphs
Linear Algebra and its Applications, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xuezhong, Tan, Liu, Bolian
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The Largest Laplacian Spectral Radius of Unicyclic Graphs with Fixed Diameter
Journal of Applied Mathematics, 2013 We identify graphs with the maximal Laplacian spectral radius among all unicyclic graphs with n vertices and diameter d.
Haixia Zhang
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Zagreb Indices of Trees, Unicyclic and Bicyclic Graphs With Given (Total) Domination
IEEE Access, 2019 Let G = (V, E) be a (molecular) graph. For a family of graphs G, the first Zagreb index M1 and the second Zagreb index M2 have already studied. In particular, it has been presented, the first Zagreb index M1 and the second Zagreb index M2 of trees T in ...
Doost Ali Mojdeh +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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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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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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Extremal Permanents of Laplacian Matrices of Unicyclic Graphs
AxiomsThe extremal problem of Laplacian permanents of graphs is a classical and challenging topic in algebraic combinatorics, where the inherent #P-complete complexity of permanent computation renders this pursuit particularly intractable.
Tingzeng Wu +2 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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Further Results on the Resistance-Harary Index of Unicyclic Graphs
Mathematics, 2019 The Resistance-Harary index of a connected graph G is defined as R H ( G ) = ∑ { u , v } ⊆ V ( G ) 1 r ( u , v ) , where r ( u , v ) is the resistance distance between vertices u and v in G.
Jian Lu +4 more
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Edge colouring line graphs of unicyclic graphs
Discrete Applied Mathematics, 1992 A characterization of line graphs of unicyclic graphs is established, and it is proved that the line graph \(G\) of a unicyclic graph is in class 1 unless \(G\) is an odd cycle and an optimal edge colouring of the line graph of a unicyclic graph can be computed in time \(O(| E|)\) (note that the chromatic index problem is known to be \(NP\)-complete ...
Leizhen Cai, John A. Ellis
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