Title of article
Graphs with fixed number of pendent vertices and minimal first Zagreb index
Author/Authors
GUTMAN, Ivan University of Kragujevac - Faculty of Science, Serbia , GUTMAN, Ivan State University Novi Pazar, Serbia , KAMRAN JAMIL, Muhammad Government College University - Abdus Salam School of Mathematical Sciences, Pakistan , AKHTER, Naveed Government College University - Abdus Salam School of Mathematical Sciences, Pakistan
From page
43
To page
48
Abstract
The first Zagreb index M1 of a graph G is equal to the sum of squares of degrees of the vertices of G. Goubko proved that for trees with n1 pendent vertices, M1 ≥ 9 n1 − 16. We show how this result can be extended to hold for any connected graph with cyclomatic number γ ≥ 0. In addition, graphs with n vertices, n1 pendent vertices, cyclomatic number γ, and minimal M1 are characterized. Explicit expressions for minimal M1 are given for γ = 0, 1, 2, which directly can be extended for γ 2.
Keywords
degree (of vertex) , Zagreb index , first Zagreb index , extremal graphs
Journal title
Transactions on Combinatorics
Journal title
Transactions on Combinatorics
Record number
2536804
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