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Degree Condition for Subdivisions of Unicyclic Graphs
Graphs and Combinatorics, 2008The authors prove the following results: Let \(H\) be any graph of order \(n\) with \(k\) vertex disjoint pieces \(H_1,\dots, H_k\), each of which contains at most one cycle. Let \(G\) be any graph of order at least \(n\) with \(\delta (G) \geq n -k \). Then \(G\) contains a cyclic subdivision of \(H\).
BABU, C, DIWAN, A
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Euler Sombor Index of Trees, Unicyclic and Chemical Graphs
Match-communications in Mathematical and in Computer ChemistryRecently, Tang et al. observed the chemical applicability of the Euler Sombor index, is potentially a very good molecular descriptor since it correlates well with the properties of octane isomers.
Biswaranjan Khanra, Shibsankar Das
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REDUCED SECOND ZAGREB INDEX OF UNICYCLIC GRAPHS
Advances and Applications in Discrete Mathematics, 2018Summary: Recently a novel degree based topological index, reduced second Zagreb index, defined for any connected graph as follows: \[RM_2=\sum_{uv\in E(G)}\,(d_u-1)(d_v-1), \] where \(d_u\) and \(d_v\) are the number of edges incident to the vertices \(u\) and \(v\), respectively.
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Unicycle graphs with extremal Merrifield–Simmons Index
Journal of Mathematical Chemistry, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Hongzhuan, Hua, Hongbo
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On unicyclic graphs with a given girth and their minimum symmetric division deg index
Discrete Mathematics LettersThe degree of a vertex u in a graph G is denoted by d G ( u ) . The symmetric division deg (SDD) index of G is denoted by SDD ( G ) and is defined as SDD ( G ) = (cid:80) xy ∈ E ( G ) [ d G ( x ) /d G ( y ) + d G ( y ) /d G ( x )] , where E ( G ) is the ...
Palaniyappan Nithya +5 more
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Mathematics
Consider a unicyclic graph G with edge set E(G). Let f be a real-valued symmetric function defined on the Cartesian square of the set of all distinct elements of G’s degree sequence. A graphical edge-weight-function index of G is defined as If(G)=∑xy∈E(G)
Akbar Ali +3 more
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Consider a unicyclic graph G with edge set E(G). Let f be a real-valued symmetric function defined on the Cartesian square of the set of all distinct elements of G’s degree sequence. A graphical edge-weight-function index of G is defined as If(G)=∑xy∈E(G)
Akbar Ali +3 more
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Linear and multilinear algebra
The smallest positive eigenvalue $ \tau (G) $ τ(G) of a simple graph G is the smallest positive eigenvalue of its adjacency matrix $ A(G) $ A(G). In [F. J. Zhang and A.
S. Barik +2 more
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The smallest positive eigenvalue $ \tau (G) $ τ(G) of a simple graph G is the smallest positive eigenvalue of its adjacency matrix $ A(G) $ A(G). In [F. J. Zhang and A.
S. Barik +2 more
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Largest eigenvalue of a unicyclic mixed graph
Applied Mathematics-A Journal of Chinese Universities, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Minimal configuration unicyclic graphs
Linear and Multilinear Algebra, 2009Milan Nath, Bhaba Kumar Sarma
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Zagreb-Eccentricity Indices of Unicyclic Graph with Application to Cycloalkanes
, 2016R. S. Haoer +4 more
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