Results 51 to 60 of about 2,717 (193)
A survey and a new class of graceful unicylic graphs
AKCE International Journal of Graphs and Combinatorics, 2020 A graph G admits a graceful labeling if there is a one-to-one map f from the set of vertices of G to such that when an edge xy is assigned the label the resulting set of edge labels is When such a labeling exists, G is called graceful. Rosa showed that a
Max Pambe Biatch’ +2 more
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Maximizing spectral radii of uniform hypergraphs with few edges
, 2015 In this paper we investigate the hypergraphs whose spectral radii attain the maximum among all uniform hypergraphs with given number of edges. In particular we characterize the hypergraph(s) with maximum spectral radius over all unicyclic hypergraphs ...
Fan, Yi-Zheng +3 more
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Journal of Applied Mathematics, 2012 Let Φ(G,λ)=det(λIn-L(G))=∑k=0n(-1)kck(G)λn-k be the characteristic polynomial of the Laplacian matrix of a graph G of order n. In this paper, we give four transforms on graphs that decrease all Laplacian coefficients ck(G) and investigate a conjecture A.
Xinying Pai, Sanyang Liu
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A Comparison between the Metric Dimension and Zero Forcing Number of Trees and Unicyclic Graphs
, 2017 The \emph{metric dimension} $\dim(G)$ of a graph $G$ is the minimum number of vertices such that every vertex of $G$ is uniquely determined by its vector of distances to the chosen vertices.
Eroh, Linda, Kang, Cong X., Yi, Eunjeong
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Laplacian Spectral Characterization of Some Unicyclic Graphs
Journal of Applied Mathematics, 2014 Let W(n;q,m1,m2) be the unicyclic graph with n vertices obtained by attaching two paths of lengths m1 and m2 at two adjacent vertices of cycle Cq. Let U(n;q,m1,m2,…,ms) be the unicyclic graph with n vertices obtained by attaching s paths of lengths m1,m2,
Lijun Yu, Hui Wang, Jiang Zhou
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The Second Maximum Mostar Index of Unicyclic Graphs With Given Diameter
Journal of Mathematics, Volume 2026, Issue 1, 2026.Topological invariants are key tools for studying the physicochemical and thermodynamic properties of chemical compounds. Recently, a new bond‐additive distance‐based graph invariant called the Mostar index has been developed. It measures the importance of individual edges and the graph as a whole. It is denoted and defined as MoG=∑xy∈EGnxxy−nyxy. This
Muhammad Amer Qureshi +5 more
wiley +1 more source
Problems on Matchings and Independent Sets of a Graph
, 2018 Let $G$ be a finite simple graph. For $X \subset V(G)$, the difference of $X$, $d(X) := |X| - |N (X)|$ where $N(X)$ is the neighborhood of $X$ and $\max \, \{d(X):X\subset V(G)\}$ is called the critical difference of $G$. $X$ is called a critical set if $
Bhattacharya, Amitava +2 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
wiley +1 more source
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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Eccentric connectivity index [PDF]
, 2010 The eccentric connectivity index $\xi^c$ is a novel distance--based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. It is defined as $\xi^c (G) = \sum_{v \in V (G)} deg (v) \cdot
Ilić, Aleksandar
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