We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
GRAPHS WITH FIXED NUMBER OF PENDENT VERTICES AND MINIMAL FIRST ZAGREB INDEX.
- Authors
GUTMAN, I.; KAMRAN JAMIL, M.; AKHTER, N.
- 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.
- Subjects
GRAPHIC methods; MATHEMATICAL models; GEOMETRIC vertices; MATHEMATICAL statistics; MATHEMATICAL functions
- Publication
Transactions on Combinatorics, 2015, Vol 4, Issue 1, p43
- ISSN
2251-8657
- Publication type
Article