Upper bounds for the reduced second zagreb index of graphs
Publish place: Transactions on Combinatorics، Vol: 10، Issue: 3
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_COMB-10-3_001
تاریخ نمایه سازی: 17 خرداد 1400
Abstract:
The graph invariant RM_۲, known under the name reduced second Zagreb index, is defined as RM_۲(G)=\sum_{uv\in E(G)}(d_G(u)-۱)(d_G(v)-۱), where d_G(v) is the degree of the vertex v of the graph G. In this paper, we give a tight upper bound of RM_۲ for the class of graphs of order n and size m with at least one dominating vertex. Also, we obtain sharp upper bounds on RM_۲ for all graphs of order n with k dominating vertices and for all graphs of order n with k pendant vertices. Finally, we give a sharp upper bound on RM_۲ for all k-apex trees of order n. Moreover, the corresponding extremal graphs are characterized.
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Authors
Batmend Horoldagva
Department of Mathematics, Mongolian National University of Education, Baga toiruu-۱۴, Ulaanbaatar, Mongolia
Tsend-Ayush Selenge
Department of Mathematics, National University of Mongolia, P.O.Box ۱۸۷/۴۶A, Ulaanbaatar, Mongolia
Lkhagva Buyantogtokh
Department of Mathematics, Mongolian National University of Education, Baga toiruu-۱۴, Ulaanbaatar, Mongolia
Shiikhar Dorjsembe
Department of Mathematics, Mongolian National University of Education, Baga toiruu-۱۴, Ulaanbaatar, Mongolia