The maximum size of a nonhamiltonian-connected graph with given order and minimum degree

TL;DR

This paper determines the maximum number of edges in nonhamiltonian-connected graphs with specified order and minimum degree, extending classical theorems and characterizing extremal graphs.

Contribution

It generalizes previous results by establishing the maximum size and characterizing extremal graphs for nonhamiltonian-connected graphs with given parameters.

Findings

Maximum size of such graphs is determined.

Extremal graphs that attain this maximum are characterized.

Results extend classical theorems by Ore and others.

Abstract

In this paper, we determine the maximum size of a nonhamiltonian-connected graph with prescribed order and minimum degree. We also characterize the extremal graphs that attain this maximum size. This work generalizes a previous result obtained by Ore [ J. Math. Pures Appl. 42 (1963) 21-27] and further extends a theorem proved by Ho, Lin, Tan, Hsu, and Hsu [Appl. Math. Lett. 23 (2010) 26-29]. As a corollary of our main result, we determine the maximum size of a $k$-connected nonhamiltonian-connected graph with a given order.