We prove that the coindex of the box complex B(H) of a graph H can be measured by the generalised Mycielski graphs which admit a homomorphism to it. As a consequence, we exhibit for every graph H a system of linear equations solvable in polynomial time, with the following properties: If the system has no solutions, then coind(B(H))+2 ≤ 3; if the system has solutions, then χ(H) ≥ 4. We generalis...

Abstract Any 6-dimensional strict nearly Kähler manifold is Einstein with positive scalar curvature. We compute the coindex of metric respect to Einstein–Hilbert functional on each compact homogeneous examples. Moreover, we show that infinitesimal deformations $$F_{1,2}={\text {SU}}(3)/T^2$$ F <mml:...

Recently introduced Zagreb coindices are a generalization of classical Zagreb indices of chemical graph theory. We explore here their basic mathematical properties and present explicit formulae for these new graph invariants under several graph operations.

Naveed Latif,1 J. Pečarić,1, 2 and I. Perić3 1 Abdus Salam School of Mathematical Sciences, GC University, Lahore 54000, Pakistan 2 Faculty of Textile Technology, University of Zagreb, 10000 Zagreb, Croatia 3 Faculty of Food Technology and Biotechnology, University of Zagreb, 10000 Zagreb, Croatia Correspondence should be addressed to Naveed Latif, [email protected] Received 31 July 2008;...

Ottó Dóka1*, Gitta Ficzek2, Svjetlana Luterotti3, Dane Bicanic4,5, Ruud Spruijt4, Josephus G. Buijnsters6, László Szalay2 and György Végvári2 Department of Physics and Mathematics, University of West Hungary, Deák F. sq. 1, HU-9200 Mosonmagyaróvár, Hungary Department of Fruit Science, Corvinus University, Villányi str. 29–43, HU-1118 Budapest, Hungary Faculty of Pharmacy and Biochemistry, Unive...

The study by da Cunha et al. published in 2002 reported that MMR vaccine containing L-Zagreb mumps strain manufactured by Serum Institute of India Ltd. caused a high incidence of aseptic meningitis (AM) from routine surveillance during two mass immunization campaigns (MIC) conducted in 1998 in two states in Brazil. Since the results were contrary to those in India, Egypt and Bahamas, a critical...

The first reformulated Zagreb index $EM_1(G)$ of a simple graph $G$ is defined as the sum of the terms $(d_u+d_v-2)^2$ over all edges $uv$ of $G .$ In this paper, the various upper and lower bounds for the first reformulated Zagreb index of a connected graph interms of other topological indices are obtained.

Topological indices are widely used as mathematical tools to analyze different types of graphs emerged in a broad range of applications. The Hyper-Zagreb index (HM) is an important tool because it integrates the first two Zagreb indices. In this paper, we characterize the trees and unicyclic graphs with the first four and first eight greatest HM-value, respectively.

The first general Zagreb index is defined as $M_1^lambda(G)=sum_{vin V(G)}d_{G}(v)^lambda$. The case $lambda=3$, is called F-index. Similarly, reformulated first general Zagreb index is defined in terms of edge-drees as $EM_1^lambda(G)=sum_{ein E(G)}d_{G}(e)^lambda$ and the reformulated F-index is $RF(G)=sum_{ein E(G)}d_{G}(e)^3$. In this paper, we compute the reformulated F-index for some grap...

For a graph $G$ with edge set $E(G)$, the multiplicative sum Zagreb index of $G$ is defined as$Pi^*(G)=Pi_{uvin E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$.In this paper, we first introduce some graph transformations that decreasethis index. In application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum Zagreb ...