Results 151 to 160 of about 3,013 (185)

Trees and Unicyclic Graphs

The Mathematics Teacher, 1967
There are many results in mathematics that are both new and elementary. Graph theory, which abounds in theorems of this kind, is the source of an interesting self-contained example which we present in this article.
Sabra S. Anderson, Frank Harary
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Unicyclic nonintegral sum graphs

Journal of Applied and Industrial Mathematics, 2008
A graph G = (V,E) is an integral sum graph if there exists a labeling S(G) ⊂ Z such that V = S(G) and every two distinct vertices u, υ ∈ V are adjacent if and only if u + υ ∈ V. A connected graph G = (V,E) is called unicyclic if |V| = |E|. In this paper two infinite series are constructed of unicyclic graphs that are not integral sum graphs.
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Trees and unicyclic graphs with hamiltonian path graphs

Journal of Graph Theory, 1990
AbstractWe prove two conjectures of Broersma and Hoede about path graphs of trees and unicyclic graphs.
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On broadcasting in unicyclic graphs

Journal of Combinatorial Optimization, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Harutyunyan, Hovhannes A., Maraachlian, Edward   +1 more
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Extreme Sombor Spectral Radius of Unicyclic Graphs

Match Communications in Mathematical and in Computer Chemistry, 2023
Summary: Let \(G\) be a graph, the Sombor matrix \(S(G)\) of \(G\) was recently introduced by \textit{Z. Wang} et al. [``Spectral radius and energy of Sombor matrix of graphs'', Filomat 35, No. 15, 5093--5100 (2021; \url{doi:10.2298/FIL2115093W}]. It is a new matrix based on Sombor index, where the \((i,j)\) entry \(S_{ij}=\sqrt{d_i^2+d_j^2}\) if ...
Mei, Yinzhen, Fu, Huifeng, Miao, Hongli, Gao, Yubin   +3 more
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THE GUTMAN INDEX OF UNICYCLIC GRAPHS

Discrete Mathematics, Algorithms and Applications, 2012
Let G be a connected graph with vertex set V(G). The Gutman index of G is defined as S(G) = ∑{u, v}⊆V(G) d(u)d(v)d(u, v), where d(u) is the degree of vertex u, and d(u, v) denotes the distance between u and v. In this paper, we characterize n-vertex unicyclic graphs with girth k, having minimal Gutman index.
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Roman domination in unicyclic graphs

Journal of Discrete Mathematical Sciences and Cryptography, 2012
Abstract A Roman dominating function on a graph G = (V, E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f (v) = 2. The weight of a Roman dominating function is the value w (f) = ∑ u∈V f(u).
P. Roushini Leely Pushpam, T. N. M. Malini Mai   +1 more
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EXTREMAL IRREGULARITY OF TOTALLY SEGREGATED UNICYCLIC GRAPHS

Far East Journal of Mathematical Sciences (FJMS), 2019
Summary: The irregularity of a simple graph \(G=(V,E)\) is defined as \(irr(G)=\sum_{uv\in E(G)}|\mathrm{deg}_G(v)|\), where \(\mathrm{deg}_G(u)\) denotes the degree of a vertex \(u\in V(G)\). A graph in which any two adjacent vertices have distinct degrees is a totally segregated graph. In this paper we determine maximum and minimum of \(\{irr(G): \ G
Jorry, T. F., Parvathy, K. S.
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Degree Condition for Subdivisions of Unicyclic Graphs

Graphs and Combinatorics, 2008
The 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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REDUCED SECOND ZAGREB INDEX OF UNICYCLIC GRAPHS

Advances and Applications in Discrete Mathematics, 2018
Summary: 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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