Results 51 to 60 of about 298 (175)
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
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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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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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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 ...
Cai, Leizhen, Ellis, John A.
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Recognizing Trees From Incomplete Decks
Journal of Graph Theory, Volume 110, Issue 3, Page 322-336, November 2025.ABSTRACT Given a graph G, the unlabeled subgraphs G − v are called the cards of G. The deck of G is the multiset { G − v : v ∈ V ( G ) }. Wendy Myrvold showed that a disconnected graph and a connected graph both on n vertices have at most ⌊ n 2 ⌋ + 1 cards in common and found (infinite) families of trees and disconnected forests for which this upper ...
Gabriëlle Zwaneveld
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On 2-power unicyclic cubic graphs
Electronic Journal of Graph Theory and Applications, 2022 In a graph, a cycle whose length is a power of two (that is, 2k) is called a 2-power cycle. In this paper, we show that the existence of an infinite family of cubic graphs which contain only one cycle whose length is a power of 2.
Shariefuddin Pirzada +2 more
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The Moran Process on a Random Graph
Random Structures &Algorithms, Volume 66, Issue 3, May 2025.ABSTRACT We study the fixation probability for two versions of the Moran process on the random graph Gn,p$$ {G}_{n,p} $$ at the threshold for connectivity. The Moran process models the spread of a mutant population in a network. Throughout the process, there are vertices of two types, mutants, and non‐mutants.
Alan Frieze, Wesley Pegden
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