The Number of 1-Nearly Independent Edge Subsets

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Andriantiana Eric O‎. ‎D‎. ‎; ‎Shozi Zekhaya B‎.

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Journal Paper

Paper Information

Journal: Iranian Journal of Mathematical Chemistry Year:2025 | Volume:16 | Issue:1 Page(s): 65-84

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Information Journal Paper

Title

The Number of 1-Nearly Independent Edge Subsets

Author(s)

Andriantiana Eric O‎. ‎D‎. ‎ | ‎Shozi Zekhaya B‎. | Issue Writer Certificate

Keywords

1-Nearly independent edge subset

Minimal graphs

Maximal graphs

Abstract

Let G = (V (G), E(G)) be a graph with the set of vertices V (G) and the set of edges E(G). A subset S of E(G) is called a k-nearly independent edge subset if there are exactly k pairs of elements of S that share a common end. Zk(G) is the number of such subsets. This paper studies Z1. Various properties of Z1 are discussed. We characterize the two n-vertex trees with the smallest Z1, as well as the one with the largest value. A conjecture on the n-vertex tree with the second-largest Z1 is proposed.

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