Displaying similar documents to “Nordhaus-Gaddum-Type Results for Resistance Distance-Based Graph Invariants”

Further results on sequentially additive graphs

Suresh Manjanath Hegde, Mirka Miller (2007)

Discussiones Mathematicae Graph Theory

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Given a graph G with p vertices, q edges and a positive integer k, a k-sequentially additive labeling of G is an assignment of distinct numbers k,k+1,k+2,...,k+p+q-1 to the p+q elements of G so that every edge uv of G receives the sum of the numbers assigned to the vertices u and v. A graph which admits such an assignment to its elements is called a k-sequentially additive graph. In this paper, we give an upper bound for k with respect to which the given graph may possibly be k-sequentially...

Variable neighborhood search for extremal graphs. 17. Further conjectures and results about the index

Mustapha Aouchiche, Pierre Hansen, Dragan Stevanović (2009)

Discussiones Mathematicae Graph Theory

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The AutoGraphiX 2 system is used to compare the index of a connected graph G with a number of other graph theoretical invariants, i.e., chromatic number, maximum, minimum and average degree, diameter, radius, average distance, independence and domination numbers. In each case, best possible lower and upper bounds, in terms of the order of G, are sought for sums, differences, ratios and products of the index and another invariant. There are 72 cases altogether: in 7 cases known results...

The Distance Magic Index of a Graph

Aloysius Godinho, Tarkeshwar Singh, S. Arumugam (2018)

Discussiones Mathematicae Graph Theory

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Let G be a graph of order n and let S be a set of positive integers with |S| = n. Then G is said to be S-magic if there exists a bijection ϕ : V (G) → S satisfying ∑x∈N(u) ϕ(x) = k (a constant) for every u ∈ V (G). Let α(S) = max{s : s ∈ S}. Let i(G) = min α(S), where the minimum is taken over all sets S for which the graph G admits an S-magic labeling. Then i(G) − n is called the distance magic index of the graph G. In this paper we determine the distance magic index of trees and complete...

Generalized outerplanar index of a graph

Zahra Barati (2018)

Czechoslovak Mathematical Journal

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We define the generalized outerplanar index of a graph and give a full characterization of graphs with respect to this index.

A note on degree-continuous graphs

Chiang Lin, Wei-Bo Ou (2007)

Czechoslovak Mathematical Journal

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The minimum orders of degree-continuous graphs with prescribed degree sets were investigated by Gimbel and Zhang, Czechoslovak Math. J. 51 (126) (2001), 163–171. The minimum orders were not completely determined in some cases. In this note, the exact values of the minimum orders for these cases are obtained by giving improved upper bounds.

On the adjacent eccentric distance sum of graphs

Halina Bielak, Katarzyna Wolska (2015)

Annales UMCS, Mathematica

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In this paper we show bounds for the adjacent eccentric distance sum of graphs in terms of Wiener index, maximum degree and minimum degree. We extend some earlier results of Hua and Yu [Bounds for the Adjacent Eccentric Distance Sum, International Mathematical Forum. Vol. 7 (2O02) no. 26. 1280-1294]. The adjaceni eccentric distance sum index of the graph G is defined as [...] where ε(υ) is the eccentricity of the vertex υ, deg(υ) is the degree of the vertex υ and D(υ) = ∑u∊v(G) d (u,υ)is...

Degree Sequences of Monocore Graphs

Allan Bickle (2014)

Discussiones Mathematicae Graph Theory

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A k-monocore graph is a graph which has its minimum degree and degeneracy both equal to k. Integer sequences that can be the degree sequence of some k-monocore graph are characterized as follows. A nonincreasing sequence of integers d0, . . . , dn is the degree sequence of some k-monocore graph G, 0 ≤ k ≤ n − 1, if and only if k ≤ di ≤ min {n − 1, k + n − i} and ⨊di = 2m, where m satisfies [...] ≤ m ≤ k ・ n − [...] .

Minimal forbidden subgraphs of reducible graph properties

Amelie J. Berger (2001)

Discussiones Mathematicae Graph Theory

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A property of graphs is any class of graphs closed under isomorphism. Let ₁,₂,...,ₙ be properties of graphs. A graph G is (₁,₂,...,ₙ)-partitionable if the vertex set V(G) can be partitioned into n sets, V₁,V₂,..., Vₙ, such that for each i = 1,2,...,n, the graph G [ V i ] ∈ i . We write ₁∘₂∘...∘ₙ for the property of all graphs which have a (₁,₂,...,ₙ)-partition. An additive induced-hereditary property is called reducible if there exist additive induced-hereditary properties ₁ and ₂ such that = ₁∘₂....