On Conjectures of Graffiti

Fajtlowicz, Siemion

doi:10.1016/s0167-5060(08)70776-3

Cited by 123 publications

(133 citation statements)

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“…Moreover, the equality holds in (18) if and only if G is a regular graph, by Theorem 2.3 (i) and the proof of Theorem 3.1.…”

Section: Corollary 33mentioning

confidence: 75%

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Zagreb indices of graphs

Das

Nam

2015

Front. Math. China

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The first Zagreb index M 1 (G) is equal to the sum of squares of the degrees of the vertices, and the second Zagreb index M 2 (G) is equal to the sum of the products of the degrees of pairs of adjacent vertices of the underlying molecular graph G. In this paper, we obtain lower and upper bounds on the first Zagreb index M 1 (G) of G in terms of the number of vertices (n), number of edges (m), maximum vertex degree (Δ), and minimum vertex degree (δ). Using this result, we find lower and upper bounds on M 2 (G). Also, we present lower and upper bounds on M 2 (G) + M 2 (G) in terms of n, m, Δ, and δ, where G denotes the complement of G. Moreover, we determine the bounds on first Zagreb coindex M 1 (G) and second Zagreb coindex M 2 (G). Finally, we give a relation between the first Zagreb index and the second Zagreb index of graph G.

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“…Moreover, the equality holds in (18) if and only if G is a regular graph, by Theorem 2.3 (i) and the proof of Theorem 3.1.…”

Section: Corollary 33mentioning

confidence: 75%

“…The inverse degree first attracted attention through conjectures of the computer program Graffiti [18]. It has been studied by several authors, see, for example, [7,8,17].…”

mentioning

confidence: 99%

Zagreb indices of graphs

Das

Nam

2015

Front. Math. China

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show abstract

“…A number of systems has been developed for performing automated concept formation in mathematics, including (Colton, 2002;Epstein, 1988;Fajtlowicz, 1988;Lenat, 1976;Sims & Bresina, 1989). Usually, they explore a domain empirically and construct concepts which describe subsets of the domain they are working in.…”

Section: Conceptual Blending and Hdtpmentioning

confidence: 99%

A computational account of conceptual blending in basic mathematics

Guhe

Pease

Smaill

et al. 2011

Cognitive Systems Research

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“…This index first appeared in [5] and was studied for simple connected graphs and trees in [17]. Several extremal properties of the sum-connectivity and general sum-connectivity index for trees, unicyclic graphs and general graphs were given in [3,4,16,18,19].…”

Section: Introductionmentioning

confidence: 99%