Results 71 to 80 of about 342,995 (169)

Bounds on the Signed 2-Independence Number in Graphs

Discussiones Mathematicae Graph Theory, 2013
Let G be a finite and simple graph with vertex set V (G), and let f V (G) → {−1, 1} be a two-valued function. If ∑x∈N|v| f(x) ≤ 1 for each v ∈ V (G), where N[v] is the closed neighborhood of v, then f is a signed 2-independence function on G.
Volkmann Lutz
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On the Signed (Total) K-Independence Number in Graphs

Discussiones Mathematicae Graph Theory, 2015
Let G be a graph. A function f : V (G) → {−1, 1} is a signed k- independence function if the sum of its function values over any closed neighborhood is at most k − 1, where k ≥ 2.
Khodkar Abdollah, Samadi Babak, Volkmann Lutz   +2 more
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Average distance and independence number

Discrete Applied Mathematics, 1994
For a connected graph \(G\) of order \(n\), the average distance \(\mu(G)\) is defined as \[ \mu(G)= \left({n\atop 2}\right)^{-1} \sum_{u,v\in V(G)} d(u,v), \] where \(d(u,v)\) denotes the length of a shortest path joining the vertices \(u\) and \(v\).
openaire   +1 more source

New Formulae for the Decycling Number of Graphs

Discussiones Mathematicae Graph Theory, 2019
A set S of vertices of a graph G is called a decycling set if G−S is acyclic. The minimum order of a decycling set is called the decycling number of G, and denoted by ∇(G). Our results include: (a) For any graph G,, where T is taken over all the spanning
Yang Chao, Ren Han
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Subgroup intersection graph of finite abelian groups [PDF]

Transactions on Combinatorics, 2012
Let G be a finite group with identity e. The subgroup intersection graph Gamma_SI (G) of G isa graph with vertex set G − e and two distinct vertices x and y are adjacent if and only if | i ∩ | | > 1.
T. Tamizh Chelvam, M. Sattanathan
doaj  

Independence Number in Path Graphs

COMPUTING AND INFORMATICS, 2012
In the paper we present results, which allow us to compute the independence numbers of $P_2$-path graphs and $P_3$-path graphs of special graphs. As $P_2(G)$ and $P_3(G)$ are subgraphs of iterated line graphs $L^2(G)$ and $L^3(G)$, respectively, we compare our results with the independence numbers of corresponding iterated line graphs.
Martin Knor, Ľudovít Niepel
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Linear independence of trigonometric numbers

, 2015
Given any two rational numbers $r_1$ and $r_2$, a necessary and sufficient condition is established for the three numbers $1$, $\cos ( r_1)$, and $\cos ( r_2)$ to be rationally independent. Extending a classical fact sometimes attributed to I. Niven, the result even yields linear independence over larger number fields. The tools employed in the proof
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Extremal k-Connected Graphs with Maximum Closeness

Axioms
Closeness is a measure that quantifies how quickly information can spread from a given node to all other nodes in the network, reflecting the efficiency of communication within the network by indicating how close a node is to all other nodes. For a graph
Fazal Hayat, Daniele Ettore Otera
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On k-prime graphs

Open Mathematics
In the context of a simple undirected graph GG, a kk-prime labeling refers to assigning distinct integers from the set {k,k+1,…,∣V(G)∣+k−1}\left\{k,k+1,\ldots ,| V\left(G)| +k-1\right\} to its vertices, such that adjacent vertices in GG are labeled with ...
Abughneim Omar A., Abughazaleh Baha’
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Approximating Vizing's independence number conjecture

, 2016
Revised version: The title is ...
openaire   +3 more sources