A layered directed acyclic graph (DAG) is a DAG the vertices of which are placed ... level is called a layer and a partition of the vertex set of a DAG into layers is.
In this paper, we determine an exact value of edge irregularity strength for triangular ..... r. 2. â(m â 1) + â j + r â 1. 2. â, if i is odd i â 2. 2. (5m â 2) + 4m + r â â.
Keywords: irregularity measures of graph; topological graph indices. 1 Introduction ..... ization of G(2, x, y) graphs, in such a way that the vertex set U induces a.
Jun 3, 2015 - |dG(u) â dG(v)|. In [2], Albertson defined the irregularity of G as. B Nilanjan De [email protected]. Anita Pal [email protected].
Journal of Algorithms and Computation journal homepage: http://jac.ut.ac.ir. Total vertex irregularity strength of corona product of some graphs. P. Jeyanthiâ1 ...
Jul 4, 2014 - We show that Conjecture 1.1 is true only for non-regular connected ... Proof. Assume that the claim of the proposition is false, i.e., D(G) = {d1,d2,...,dk}, ..... [10] L. Collatz, U. Sinogowitz, Spektren endlicher Graphen, Abh. Math.
Abstract. Albertson [3] has defined the irregularity of a simple undirected graph G = (V, E) as irr(G) = ... For general graphs with n vertices, Albertson has obtained.
Gary Ebert, Joe Henimeter, Felix Lazebnik, Andrew Woldar. ABSTRACT ... For each vertex v of G, we deï¬ne the weight wt(v) of v in G(w) by. 1015(1)) = 2 40(6),.
Jul 4, 2014 - The latter measurement was introduced by Albertson [5] and investigated in several works including [1,13,14]. For motivations of introducing the ...
Apr 2, 2013 - join of a graph with itself, complete bipartite graphs, and cycles, this minimum value is obtained. ...... [15] C. Johnson, R. Loewy and P.A. Smith.
Oct 9, 2018 - problem of choosing an ideal cycle decomposition is addressed and is pre- sented as an ... The decycling number of a graph, â(G), is the size of a smallest decycling set. ..... Spring School And International Conference On Combinatori
irregular total k-labeling of the graph G if for every two different vertices x and y of ... came from irregular assignments and the irregularity strength of graphs ...
E-Mail: [email protected]. URL: http://www.tbi.univie.ac.at/~studla. cThe Santa Fe Institute,. 1399 Hyde Park Road, Santa Fe, NM 87501, USA. Abstract.
Feb 8, 2007 - and DMS-0600303, UIUC Campus Research Board 06139 and 07048, and OTKA 049398. †University of Illinois at Urbana-Champaign, ...
since all C4-saturated graphs are P3-connected, this is a generalization of ... most three from v, all nodes other than w and v are in X or Y . Thus. jXj + jY j = n ? 2.
Feb 2, 1999 - Note that we have de ned at most blog nc ... Each gadget is composed of twelve independent sets of vertices containing no internal edges ( ...
On The Total Irregularity Strength of Regular Graphs - CORE › publication › fulltext › On-The-T... › publication › fulltext › On-The-T...by R Ramdani · 2015 · Cited by 9 · Related articles 2. Keywords: cycle; dual labeling; path; prism; regular gr
Arthur M. Farley and Andrzej Proskurowski. Computer and Information Science Department. University of Oregon. Eugene, Oregon 97403, USA. Abstract.
The Iitaka fibration associated to L is a birational model of the map induced by the linear .... Consider A = E Ã E a product of elliptic cures and let M = pâ. 1H + pâ.
Sep 29, 2017 - M. The Esperanto text (L = 28) used in the analysis is La Batalo del Vivo, of Charles Dickens. For an extended ... Moby Dick (Herman Melville ).
confound the morphological properties of regular and irregular forms with their .... speakers are more likely to replace the base by an irregular form on purely.
c Computer and Automation Institute, Hungarian Academy of Sciences, ... For each vertex x of G(w), the weighted degree wt(x) is defined as the sum of the.
Intensification, 49(4), (2010), 418-424. [2] Nidal Hilal, The dependence of solid expansion on bed diameter, particles material, size and distributor in open.
Oct 13, 2007 - [3] B. Csaba, Approximating the BollobásâEldridgeâCatlin conjecture for bounded degree graphs, manuscript. [4] M. Krause, A simple proof of ...
The word graph refers to a finite, undirected graph without loops and multiple edges. For a graph G, Albertson has defined the irregularity of G as irr(G)=. | ( ).
5th Conference on Algebraic Combinatorics and Graph Theory, July 3 4, 2012
THE SECOND MINIMUM OF THE IRREGULARITY OF GRAPHS R. Nasiri-Gharghani1 and G. H. Fath-Tabar2 1
Department of Mathematics, University of Qom, Qom, Islamic Republic of Iran 2 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-51167, I. R. Iran
Abstract
The word graph refers to a finite, undirected graph without loops and multiple edges. For a graph G, Albertson has defined the irregularity of G as irr(G)=
| ( )
( )| where
d(u) is the degree of vertex u. Recently, this graph invariant gained interest in chemical graph theory. In this work, we present some new result on the second minimum of the irregularity of graphs.
Theorem 1. Let G be a graph then Irr(G) is only even number. Corollary 2. The second minimum of the irregularity of a graph is 2. Theorem 3. There are 25 types of graphs with irregularity of 2.
References 1. M. O. Albertson, The irregularity of a graph, Ars Comb. 46 (1997) 219 225. 2. G. H. Fath Tabar, B. Furtula and I. Gutman, A new geometric-arithmetic index, J. Math. Chem. 47 (2010) 477 486. 3. G. H. Fath Tabar, Old and new Zagreb index, MATCH Commun. Math.Comput. Chem. 65 (2011)79 84.
