In this paper, we introduce the concepts of minimal path cover sets and the index of

covering of a simple graph G, and study the basic properties of these notions. Corresponding

to these combinatorial concepts, we define max-path ideal...

In this paper, we study minimal path cover sets of union of certain

graphs. As consequences, we study max-path ideals with certain heights....

In this study, two developed shortest path algorithms that run fast on the real large volume road networks have been identified. The first one is heuristic genetic algorithm implemented with approximate buckets in scalar computing environment...

‎Consider an $m\\times n$ table $T$ and latices paths $\\nu_1,\\ldots,\\nu_k$ in $T$ such that each step $\\nu_{i+1}-\\nu_i=(1,1)$‎, ‎$(1,0)$ or $(1,-1)$‎. ‎The number of paths from the $(1,i)$-cell (resp‎. ‎first column) to the $(s...