曲阜师范大学学报（自然科学版）
麯阜師範大學學報（自然科學版）
곡부사범대학학보（자연과학판）
JOURNAL OF QUFU NORMAL UNIVERSITY (NATURAL SCIENCE EDITION)
2015年
1期
7-18
,共12页
Harmonic 指标%二阶 harmonic 指标%六角螺链%六角螺系统
Harmonic 指標%二階 harmonic 指標%六角螺鏈%六角螺繫統
Harmonic 지표%이계 harmonic 지표%륙각라련%륙각라계통
Harmonic index%second-order harmonic index%spiro hexagonal chains%spiro hexagonal sys-tems
图G的 Harmonic指标定义为图G 中所有边uv 的权重2du＋dv 的和，用 H（G）表示；二阶Harmonic指标被定义为图G中所有二长路uvw的权重3du＋dv＋dw 的和，用2H（G）表示；其中du表示G中点u的度数。该文研究了六角螺链和六角螺系统的 Harmonic 指标，发现它们的极图不唯一。通过研究二阶 Harmonic指标，确定了六角螺链的极图，发现六角螺系统的极图是一类特定的图。并且找到一个关于Harmonic 指标的极图和二阶 Harmonic 指标的极图的关系。最后，提出一个关于 Harmonic 指标的开放新问题。
圖G的 Harmonic指標定義為圖G 中所有邊uv 的權重2du＋dv 的和，用 H（G）錶示；二階Harmonic指標被定義為圖G中所有二長路uvw的權重3du＋dv＋dw 的和，用2H（G）錶示；其中du錶示G中點u的度數。該文研究瞭六角螺鏈和六角螺繫統的 Harmonic 指標，髮現它們的極圖不唯一。通過研究二階 Harmonic指標，確定瞭六角螺鏈的極圖，髮現六角螺繫統的極圖是一類特定的圖。併且找到一箇關于Harmonic 指標的極圖和二階 Harmonic 指標的極圖的關繫。最後，提齣一箇關于 Harmonic 指標的開放新問題。
도G적 Harmonic지표정의위도G 중소유변uv 적권중2du＋dv 적화，용 H（G）표시；이계Harmonic지표피정의위도G중소유이장로uvw적권중3du＋dv＋dw 적화，용2H（G）표시；기중du표시G중점u적도수。해문연구료륙각라련화륙각라계통적 Harmonic 지표，발현타문적겁도불유일。통과연구이계 Harmonic지표，학정료륙각라련적겁도，발현륙각라계통적겁도시일류특정적도。병차조도일개관우Harmonic 지표적겁도화이계 Harmonic 지표적겁도적관계。최후，제출일개관우 Harmonic 지표적개방신문제。
The harmonic index and the second-order harmonic index of a graph G are defined as the sum of the weight 2du+dv of all edgesuv ofG and the sum of the weight 3 du+dv+dw of all 2-length paths uvw of G ,where du is the degree of a vertexu ofG ,denoted by H (G)and 2 H (G),respectively.In this paper,con-sidered the spiro hexagonal chains and the spiro hexagonal systems of the harmonic indices H (G),and seek out their extremal graphs were not unique.According to study the second-order harmonic index 2 H (G),they determined the extremal graphs of spiro hexagonal chains and found that the extremal graphs of spiro hexagon-al systems are a class of certain graphs.Finally,found a relation between the extremal graphs of H (G)and the extremal graphs of 2 H (G).A open problem on graph with harmonic index is proposed.
