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On extremal cacti with respect to the edge Szeged index and edge-vertex Szeged index
- Source :
- Filomat. 32:4069-4078
- Publication Year :
- 2018
- Publisher :
- National Library of Serbia, 2018.
-
Abstract
- The edge Szeged index and edge-vertex Szeged index of a graph are defined as $Sz_{e}(G)=\sum\limits_{uv\in E(G)}m_{u}(uv|G)m_{v}(uv|G)$ and $Sz_{ev}(G)=\frac{1}{2} \sum\limits_{uv \in E(G)}[n_{u}(uv|G)m_{v}(uv|G)+n_{v}(uv|G)m_{u}(uv|G)],$ respectively, where $m_{u}(uv|G)$ (resp., $m_{v}(uv|G)$) is the number of edges whose distance to vertex $u$ (resp., $v$) is smaller than the distance to vertex $v$ (resp., $u$), and $n_{u}(uv|G)$ (resp., $n_{v}(uv|G)$) is the number of vertices whose distance to vertex $u$ (resp., $v$) is smaller than the distance to vertex $v$ (resp., $u$), respectively. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, the lower bounds of edge Szeged index and edge-vertex Szeged index for cacti with order $n$ and $k$ cycles are determined, and all the graphs that achieve the lower bounds are identified.<br />12 pages, 5 figures
- Subjects :
- General Mathematics
020206 networking & telecommunications
0102 computer and information sciences
02 engineering and technology
01 natural sciences
Graph
Vertex (geometry)
Combinatorics
010201 computation theory & mathematics
FOS: Mathematics
0202 electrical engineering, electronic engineering, information engineering
Mathematics - Combinatorics
Combinatorics (math.CO)
Mathematics
Subjects
Details
- ISSN :
- 24060933 and 03545180
- Volume :
- 32
- Database :
- OpenAIRE
- Journal :
- Filomat
- Accession number :
- edsair.doi.dedup.....efe579a61ab19b99ccea1fc2eb50106b