On the Number of Spanning Trees of Multi-Star Related Graphs
نویسندگان
چکیده
In this paper we compute the number of spanning trees of a specific family of graphs using techniques from linear algebra and matrix theory. More specifically, we consider the graphs that result from a complete graph K, after removing a set of edges that spans a multi-star graph K,,, (al, ~2, . , a,). We derive closed formulas for the number of spanning trees in the cases of double-star (m = 2), triple-star (m = 3), and quadruple-star (m = 4). Moreover for each case we prove that the graphs with the maximum number of spanning trees are exactly those that result when all the ais are equal. @ 1998 Elsevier Science B.V. Kqwords: Spanning trees; Multi-star graphs; Complement Spanning-Tree Matrix theorem; Combinatorial problems; Interconnection networks
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ورودعنوان ژورنال:
- Inf. Process. Lett.
دوره 65 شماره
صفحات -
تاریخ انتشار 1998